1) It was not an issue at that time. Jesus was a devout Jew who was not opposed to the Mosaic Law, in particularly the moral law. While he often attacked the traditions of the Pharisees or the human wisdom of the Sadducees, both of which had been added to the Law, he never once lifted a finger to attack anything God had written. At the time Christ lived, in the area Christ lived, and to the audience spoke to for the most part, there was not rampant homosexuality or sodomy as there was elsewhere in the world, and the question of what defined marriage was at that point not an issue. Therefore, to bring up that Jesus never spoke directly on homosexuality or same sex marriage is about as relevant as bringing up that Athanasius never spoke directly on post-modern thought.
2) Jesus still identified marriage as being between a man and a woman. When asked by the Pharisees about divorce, the following dialogue occurs:
And Pharisees came up to [Jesus] and tested him by asking, “Is it lawful to divorce one's wife for any cause?” He answered, “Have you not read that he who created them from the beginning made them male and female, and said, ‘Therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh’? So they are no longer two but one flesh. What therefore God has joined together, let not man separate.” [Matthew 19:3-6]Note that when speaking about marriage, Christ refers to Genesis 2 and states God had made mankind "male and female," and that, in regards to marriage, a man shall leave his father and mother (not simply "his guardians" or a vague "two parental units"), and hold fast not to his "significant other" or "civil union partner," but "his wife." In this context the two people "become one flesh" in marriage. Note also that Christ is speaking here entirely of a heterosexual relationship, both in regards to the parents and to the couple getting married. Therefore, Christ's view of marriage is one that was isolated to heterosexual relationships alone. There was no room for homosexual relationships.
3) Christ's handpicked leaders condemned homosexuality. The apostle Paul especially condemned it: while talking of "dishonorable passions," he makes mention of women who "exchanged natural relations" and men who "gave up natural relations with women and were consumed by passion for one another" (Rom 1:26-27); he said that those who practice homosexuality will not inherit the kingdom of God (1 Cor 6:9); he called it "contrary to sound doctrine" (1 Tim 1:10). The apostles, including Paul, were handpicked by Christ personally, and were chosen and entrusted to carry on his will and doctrine, ergo if one takes issue with how they interpret sin and morality, they shall have to take it up with Christ himself.
4) Christian theology takes into consideration the Bible as a whole. Those who might still persist in the previous point with "Paul and Co. are still not Jesus" are not considering how Christian theology views scripture as a whole, which is that all scripture is "God-breathed" and sourced directly to God (2 Tim 3:16). The only Christians who isolate doctrines to literally only the words of Christ believe what is called "Red Letterism" (referring to the habit of some Bibles to put the letters of Christ in red), and they are generally not considered orthodox in such thinking. We must also remember that Christ was God, and as all scripture is sourced to God, all scripture is therefore sourced to him, ergo we cannot isolate our inspired writ to only what words God the Son said during his earthly ministry.
Most important of all, of course, is the fact that Christ spoke out against all sin, heterosexual and homosexual alike. A man coveting after a woman for lustful purposes made him guilty of adultery, and made him just as much a sinner before God as a man embracing homosexual desires. It was for such individuals that Christ came into this world, so that he may absolve men of their sins and make them righteous before God. "I have not come to call the righteous," Christ said, "but sinners to repentance" (Luke 5:32). No man is a greater sinner than another, but "unless you repent, you will all likewise perish" (Luke 13:3). If this post has grieved anyone, I pray that it does not merely give them empty grief, but that they would be "grieved into repenting" (2 Cor 7:9), and that God may "perhaps grant them repentance leading to a knowledge of the truth" (2 Tim 2:25). One day, God will judge us all through Christ Jesus, and we will be cast either into eternal punishment or into eternal life. Until then, you have a chance to repent and place your trust in this beautiful Gospel that God has given mankind through His Christ. God bless.