Jeffersonians believe that the role of government should be carefully limited, and that its primary functions are to preserve public order and protect citizens from harm. Government is merely one aspect of society, rather than the entirety of it. Government should have the power to do only that which society wants done and which government alone can do- that, and no more. As such, 21st Century Jeffersonians hold to the opinion that the government should have no opinion whatsoever in the current debate over gay marriage, as it is not the government's place to step into disputes about morality.
Of course, homosexuality was not something widely discussed in Jefferson's time. Everyone knew about it, but it was not considered proper to discuss it openly. The only policy decision Jefferson made in his life which has any bearing on the modern public debate about homosexuality was during his time as a Virginia state legislator, when he removed sodomy from the list of crimes for which a person could be subject to the death penalty.
Jeffersonians oppose laws that attempt to ban so-called "victimless crimes". If no one is harmed by an activity, how can that activity be considered a violation of the public order, or a threat to the security of a citizen? If a man marries a man, or a woman marries a woman, how does this action victimize me? How does it victimize the person reading this blog entry? It simply does not, and therefore it should be no business of the government. After all, it is not the government's job to regulate public morality.
Under the law, citizens have the right to enter into contracts with anyone they please. If the terms of the contract do not harm anyone and if they do not disturb the public order, they cannot be considered illegal. In terms of constitutional law, it seems perfectly obvious that any laws against gay marriage are an infringement on the right of citizens to enter into contracts with other citizens, and hence are unconstitutional on the face of it.
Thomas Jefferson would rightly see the present efforts by religious fundamentalists to politicize the cultural and religious debate about homosexual marriage as the efforts by demagogues to stir up public anger purely for partisan purposes. He would see through the antics of men like Pat Robertson and James Dobson within seconds, dismissing them as the monsters they are. They and their followers of the American equivalent of Saudi Arabia's Commission for the Promotion of Virtue and the Prevention of Vice.
If Jefferson were alive today, he would keep his own personal opinions about gay marriage private, but he would oppose any efforts by state or national government to ban gay marriage as an unconstitutional assertion of power that the government does not have. From a Jeffersonian point of view, the government has no more right to regulate morality than it does to order citizens to support a particular football team.