Please read this with an open mind, this explanation must necessarily be very long—I am trying to debunk centuries of human error after all!—Mind you, all humans are full of error, except of course for one person crucified some 2,000 years ago. Don't think that I am trying to attack anyone, I am merely stating my faith, since none of us are perfect we are going to have disagreements.
I would actually say that Jesus was not silent on the issue of homosexuality. It should be mentioned that the whole idea of sexual orientation, and the term homosexuality, is quite new. "Homosexual" was not in the english language until it was coined in the late 19th century. Thus, any inclusion of the word in the Bible was added by contemporary translators to make certain passages more clear for modern readers. However, I am quite confident that a certain quote from Jesus is specifically referring to the natural nature of homosexuality, and this has not been changed to the modern word "homosexual" because of the inherent sin of humans—that is to say, the human translators refuse to include the term if its inclusion is at odds with their hatred and judgements—essentially slandering Jesus to suite their own sinful and human desires; we are all sinners and imperfect.
The quote comes from Matthew 19. The Pharisees (the most conservative. scripture-affirming sect of Jews) asked Jesus if a man could divorce his wife for any reason, which is allowed under Mosaic law in the old testament (Deut 24:1). Jesus then tells them that a man and woman become one in the eyes of god, and that you shouldn't thus split that which is one in the eyes of god. It should be noted that Jesus is explicitly disagreeing with scripture, which he does in other places, thus disproving the rather new concept of "Biblical inerrancy". It is hard for modern readers to see this, but Jesus is actually saying in his response in Matt 19:8 that "I, god, like some of the things in your scripture, but you're mostly full of s**t, listen to what I have to say". Some use Jesus's statement of "he made them man and woman" to justify their hatred against homosexuals, or that this is the only sexual orientation, but this is taken out of context: he was asked a question about husband and wife, so he gave an answer regarding husband and wife, he was not condemning homosexuals. After he says that you shouldn't divorce your wife (notwithstanding adultery), his disciples say to him that it is better not to marry. Jesus then says that not all can accept their statement: some are born eunuchs (more on this later), some are made eunuchs by others (obvious that this refers to castration), and others make themselves eunuchs for the sake of god (meaning they remain celibate, the answer his disciples have come up with), and that only people whom "god helps" can be a "religious eunuch" or someone that remains celibate for god; clearly not everybody who is saved falls into this third category. What could Jesus have possibly meant when he said that "some are born eunuchs in their mothers' wombs"? Unless he is talking about some poor toddler that suffers from erectile disfunction, or some poor fetus whose mother stuck an exact-o knife up her hoo-ha to castrate him, Jesus is clearly talking about homosexuals, and he is saying that they are born that way. Under Roman law (which provided legal definitions for all under its rule, including the jews), there were two types of eunuchs: the castrated variety, and the natural, un-castrated variety who had no interest in women (which we would now call homosexuals, what Jesus was talking about). If you don't believe me, read the Roman Legal document Lex Julia et Papia. Thus, at the very least, one has to accept that Jesus said homosexuals are born that way.
Furthermore, Jesus specifically did decry certain behaviors. For instance, Jesus says that it is not our place to judge others ( like condemning others for their sexual orientation) for we are not the judge, and that we may see the problems in others' lives but not the greater faults in our own (Matt 7, Luke 6, to name a couple places). So, even if Jesus thinks homosexuality is a sin, though I don't believe that he does, it is not our place to be the judge. In simple terms: It does nothing to serve god or his interests to judge and hate others and prevent gay people from marrying, nor does gay marriage harm straight marriage, society, or the faith and salvation of others, while there is a strong possibility one will be judged on par with their own judgment. People should question who they are serving when they don't allow gay people to live their lives in a natural way, god or their own sinful, hating nature (we all sin and hate from time to time, I am not trying to be pious or judgmental).
We know that one's sexual orientation is not a choice, but rather a complicated process of genetic and environmental causes. Talk to any gay Christian that has struggled with the issue for most of their lives, look at the overwhelming psychological and genetic evidence (the penetrance rate of homosexuality and its location on the X chromosome). Unless you are of the minority christian view that says science is wrong you must accept this (science and faith do not need to be in conflict, Jesus himself did not take old testament scripture as literal inerrant truth as evidenced by some arguments I have made, and if science is wrong then God is a liar and has gone to inconceivable lengths to obscure the truth from us). To think that people make the choice to be gay in a gay-hating society is kind of like covering your ears, closing your eyes, and going "lalalala".
On the issue of Paul, he is probably wrong. Many people say the bible (and Paul's writings in it) is the 100% inherent word of god, but this view is demonstrably incorrect. This did not become the defining, integral nature of certain Christian movements until the Niagara Creed of 1878, and the Bible is not necessary for Christianity (how else did it grow from nothing in the 3 centuries that it existed before the orthodox biblical cannon was created?). Each of the Gospels give different and sometimes contradictory accounts, and there are contradictions throughout both testaments (such as the salvation through faith alone view of Paul vs. the faith and good works view of Peter, also read Mark 2:26 and 1 Samuel 1-6 see if you can find the error). Furthermore, unless Jesus wrote something (he didn't, we only have what other people said he said), I don't care how divinely inspired you are, you are only an imperfect human and you are not capable of writing the inerrant word of god. If humans are capable of such perfect divine revelation, I question the necessity of Jesus' existence in the first place, or all of the disagreements we humans have. Paul, while divorcing Christianity from a lot of the incorrect teachings of Judaism, was an imperfect human and made some mistakes by keeping certain traditional jewish views (like ordering women to cover their head during prayer in 1 Corinthians, or the 3 statements he made from a Jewish perspective on homosexuality).
Finally, we have to ask whether homosexual marriage is a fundamentally legal or religious issue in 21st century America. Since we do not live in a Christian Theocracy, since Marriage is a legal term that influences benefits and taxation, since we are even having a discussion about the legality of gay marriage, we are talking about a fundamentally legal issue. This legal issue certainly has religious connotations within church's, but church's are allowed to limit their views on marriage in their own church, not in the country as an entirety (gay marriage would not force church's to accept and practice it, and marriages independent of any religion already exist). I hope that I have substantially made the case for Jesus's message: love, not judgment. I know most people who actually read this far will disagree with me, and that is fine—I am merely a human, I am not perfect, it is possible I have made a mistake, but it is equally as possible every other human has made a mistake as well. Have a blessed day, and praise god.