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St. Augustine:

If you wish to be a Catholic, do not venture to believe, to say, or to teach that they whom the Lord has predestinated for baptism can be snatched away from his predestination, or die before that has been accomplished in them which the Almighty has predestined.  There is in such a dogma more power than I can tell assigned to chances in opposition to the power of God, by the occurrence of which casualties that which He has predestined is not permitted to come to pass. It is hardly necessary to spend time or earnest words in cautioning the man who takes up with this error against the absolute vortex of confusion into which it will absorb him, when I shall sufficiently meet the case if I briefly warn the prudent man who is ready to receive correction against the threatening mischief.

Nothing is impossible with God, including cleansing the soul of Original Sin without water.

Why hasn't anyone responded to the link I provided?  Here is what it contained:

New post Baptism of Desire Defended
I thought it might be best to start a new thread to focus on this subject. I am confident that the correct teaching of the Church can be made clear and objections can be met.

Feeneyites usually start with Trent, so let us start there.

We understand Trent according to the definitions of Aquinas.

Trent should be understood with reference to the teaching of Aquinas, especially his Summa Theologica. The Church has told us this.

"The study of philosophy and theology and the teaching of these sciences to their students must be accurately carried out by Professors (in seminaries etc.) according to the arguments, doctrine, and principles of St. Thomas which they are inviolately to hold." Code of Canon Law, 1366, 2.

Pius X: "The reason is that the capital theses in the philosophy of St. Thomas are not to be placed in the category of opinions capable of being debated one way or another, but are to be considered as THE FOUNDATIONS upon which the whole science of natural and divine things is based; if such principles are once removed or in any way impaired, it must necessarily follow that students of the sacred sciences will ultimately FAIL TO PERCEIVE SO MUCH AS THE MEANING OF THE WORDS IN WHICH THE DOGMAS OF DIVINE REVELATION ARE PROPOSED BY THE MAGISTRACY OF THE CHURCH." (Doctoris Angelici)

So, we cannot hope to understand the dogmas of the Church without appreciating the Scholastic definitions of Aquinas. In this case, we need to understand what Aquinas means when he says that a sacrament is "necessary for salvation".

The necessity of the sacraments.

When Trent tells us that baptism is "necessary for salvation", Aquinas explains that it is necessary "either actually or in desire".

"Objection: the sacrament of Baptism is necessary for salvation. Now that is necessary “without which something cannot be” (Aristotle’s Metaphysics V). Therefore it seems that none can obtain salvation without Baptism. Reply: THE SACRAMENT OF BAPTISM IS SAID TO BE NECESSARY FOR SALVATION IN SO FAR AS THERE CAN BE NO SALVATION FOR MAN UNLESS HE AT LEAST HAVE IT IN DESIRE WHICH, WITH GOD, COUNTS FOR THE DEED." (Summa Theologica 3, 68, 2)

That is, a sacrament that is "necessary for salvation" may be received unto salvation "actually" or "in desire".

"Moreover, the SACRAMENTS of grace are ordained in order that man may receive the infusion of grace, and before HE RECEIVES THEM, EITHER ACTUALLY OR IN HIS DESIRE, he does not RECEIVE GRACE. This is evident in the case of Baptism, and applies to PENANCE likewise." (Summa Theologica, Supplement 6, 1)

Sacramental necessity at Trent.

We can see that is what Trent meant because it used the same phrase "necessary for salvation" about the sacrament of penance too -- and we all admit that one can be saved by desiring to confess if one has perfect contrition and cannot actually confess.

"And this SACRAMENT OF PENANCE is, for those who have fallen after baptism, NECESSARY FOR SALVATION, AS BAPTISM ITSELF IS for those who have not as yet been regenerated." (Denz. 895)

Although it is "necessary", it may be received in desire as well as "actually".

"Whence it is to be taught, that the penitence of a Christian, after his fall, is very different from that at (his) baptism; and that therein are included not only a cessation from sins, and a detestation thereof, or, a contrite and humble heart, but also THE SACRAMENTAL CONFESSION OF THE SAID SINS, AT LEAST IN DESIRE [saltem in voto], and to be made in its season, and sacerdotal absolution and likewise satisfaction by fasts, alms, prayers, and the other pious exercises of a spiritual life; not indeed for THE ETERNAL PUNISHMENT,-which is, together with the guilt, REMITTED, EITHER BY THE SACRAMENT, OR BY THE DESIRE OF THE SACRAMENT,-but for the temporal punishment, which, as the sacred writings teach, is not always wholly remitted, as is done in baptism." (Denz 807)

"The Synod teaches moreover, that, although it sometimes happen that this CONTRITION IS PERFECT through charity, and reconciles man with God BEFORE THIS SACRAMENT BE ACTUALLY RECEIVED, the said reconciliation, nevertheless, is not to be ascribed to that contrition, independently of THE DESIRE OF THE SACRAMENT which is included therein." (Denz. 898)

And so Aquinas.

"Moreover, the SACRAMENTS of grace are ordained in order that man may receive the infusion of grace, and before HE RECEIVES THEM, EITHER ACTUALLY OR IN HIS DESIRE, he does not RECEIVE GRACE. This is evident in the case of Baptism, and applies to PENANCE likewise." (Summa Theologica, Supplement 6, 1)

Trent told us that baptism too, may be received in "desire".

"And this translation [to the state of justification], since the promulgation of the Gospel, cannot be EFFECTED, WITHOUT THE LAVER OF REGENERATION, AT LEAST IN THE DESIRE THEREOF [aut eius voto], as it is written; “unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.” (Denz. 796)

That is usually translated as "baptism or its desire", though either translation is literal and makes the point.

And Trent told us that a third sacrament may be received in desire, even the eucharist.

"Now as to the use of this holy SACRAMENT [of the Eucharist], the Fathers have rightly and wisely distinguished THREE "WAYS OF RECEIVING IT. For they have taught that some receive it SACRAMENTALLY ONLY, to wit sinners; OTHERS SPIRITUALLY ONLY, those to wit who EATING IN DESIRE [voto] that heavenly bread which is set before them, are, by a lively faith which worketh by charity, made sensible of the fruit and usefulness thereof; whereas the third (class) receive it both SACRAMENTALLY AND SPIRITUALLY, and these are they who so prove and prepare themselves beforehand, as to approach to this divine table clothed with the wedding garment." (Denz. 881)

Aquinas likewise.

"In another way one may eat Christ spiritually, as He is under the sacramental species, inasmuch as a man believes in Christ, WHILE DESIRING TO RECEIVE THIS SACRAMENT; and this is NOT MERELY TO EAT CHRIST SPIRITUALLY, BUT LIKEWISE TO EAT THIS SACRAMENT." (Summa Theologica 3, 80, 2)

Implicit desire.

We can see the concept of implicit desire at Trent too.

Aquinas tells us that baptism can be received "in desire" when the desire is "implicit".

"Man receives the forgiveness of sins before baptism in so far as he has BAPTISM IN DESIRE, EXPLICITLY OR IMPLICITLY; and yet when he actually receives baptism, he receives a fuller remission, as to the remission of the entire punishment. So also before baptism Cornelius and others like him receive grace and virtues through their faith in Christ and THEIR DESIRE FOR BAPTISM, IMPLICIT OR EXPLICIT: but afterwards when baptized, they receive a yet greater fullness of grace and virtues." (Summa Theologica 3, 69, 4)

He gave the definition of "implicit" as when something is "contained" in something else.

"Properly speaking, that is called IMPLICIT in which many things are CONTAINED AS IN ONE, and that is called explicit in which each of the things is considered in itself." (Of Truth 14, 11)

We can see Trent employ this definition of implicit desire with reference to confession.

"The Synod teaches moreover, that, although it sometimes happen that this CONTRITION IS PERFECT through charity, and reconciles man with God BEFORE THIS SACRAMENT BE ACTUALLY RECEIVED, the said reconciliation, nevertheless, is not to be ascribed to that contrition, independently of THE DESIRE OF THE SACRAMENT WHICH IS INCLUDED THEREIN." (Denz. 898)

Moreover, when Trent said that we can be justified by baptism "or the desire thereof" (aut ejus voto) it used a phrase used by Aquinas to indicate that infants may receive the eucharist unto salvation through the desire of the Church.

"This sacrament [of the Eucharist] has, of itself, the power of bestowing grace; nor does anyone possess grace before receiving this sacrament except from some DESIRE THEREOF [ipsius voto]; from his own desire, as in the case of the adult, OR FROM THE CHURCH'S DESIRE IN THE CASE OF CHILDREN." (Summa Theologica III, 79, 1)

Necessity of sacramental matter.

Neither is it contrary to this doctrine that Trent said that water is "necessary" for baptism. It may yet be received in desire.

We may see this from that Trent said that the confession of sins individually is "necessary" for penance, yet, as we have seen, it may be received in desire as well as in act.

"From the institution of the sacrament of Penance as already explained, the universal Church has always understood, that THE ENTIRE CONFESSION OF SINS WAS ALSO INSTITUTED BY THE LORD, AND IS OF DIVINE LAW NECESSARY for all who have fallen after baptism; because that our Lord Jesus Christ, when about to ascend from earth to heaven, left priests His own vicars, as presidents and judges, unto whom all the mortal crimes, into which the faithful of Christ may have fallen, should be carried, in order that, in accordance with the power of the keys, they may pronounce the sentence of forgiveness or retention of sins. For it is manifest, that PRIESTS COULD NOT HAVE EXERCISED THIS JUDGMENT without knowledge of the cause; neither indeed could they have observed equity in enjoining punishments, if the said faithful should have declared their sins in general only, and not rather SPECIFICALLY, AND ONE BY ONE. Whence it is gathered that ALL MORTAL SINS, of which, after a diligent examination of themselves, they are conscious, MUST be by penitents enumerated in confession. [...] But, whereas all mortal sins, even those of thought, render men children of wrath, and enemies of God, it is NECESSARY TO SEEK ALSO FOR THE PARDON OF THEM ALL from God, with an open and humble confession. Wherefore, while the faithful of Christ are careful to confess all the sins which occur to their memory, they without doubt lay them all bare before the mercy of God to be pardoned." (Denz. 899)

Conclusion.

So, by reading Trent carefully, and especially with reference to the Summa, we can see that although baptism is "necessary for salvation", that is not to say that it cannot be received "in desire" unto salvation, even "implicitly" or through the desire of the Church. Indeed, we all agree that penance can be received unto salvation through desire though it is "necessary for salvation". Aquinas tells us that is true of baptism too and it is clearly the drift of Trent. The eucharist is another example.