There's a difference between what Congress has the power to do and what Congress should do.
Given the views of the primary author of the Declaration of Independence and the Statute for Virginia on Religious Freedom, it looks like the original intent of the Constitution would have allowed Congress not only to prohibit polygamy but actually to castrate all the polygamists in the federal territory of Utah.
I certainly don't advocate such things in a modern political context, and I probably wouldn't advocate them in the context of 1800s Utah, either. However, I have read books at the time of the debates over what to do with Utah arguing that Mormonism needed to be dealt with as a criminal rather than a religious matter, and I believe the federal government had the constitutional right to prohibit polygamy.
Was that a good idea in late 1800s America? Maybe yes, maybe no. In a modern political context, I've got better things to do with my time than try to prosecute breakaway non-LDS Mormon sectarian groups. Gay marriage is the pressing issue today, not plural marriage.
I do believe marriage should be limited to one man and one woman for secular, moral, and religious reasons. I believe the history of the First Amendment gives me the ability to demand far more than that, but as a matter of practical politics, I'll leave the issue there and not try to argue for prosecution of polygamists and homosexuals unless there are other crimes involved.
I trust you will recognize the allusion involved in my statement that while under the Constitution many things are lawful, not all things are helpful.
When I say that, I hope it's clear that I'm taking a position which is far more “liberal” than that of the most liberal Founding Fathers of the United States. For my position today to be considered a right-wing Christian viewpoint shows mostly how far America has fallen.