Minnesota Rep. Michele Bachmann, former Pennsylvania Senator Rick Santorum, former Minnesota Governor Tim Pawlenty, former Massachusetts Governor Mitt Romney and former House Speaker Newt Gingrich support a federal amendment defining marriage as between a man and a woman, thereby blocking gay and lesbian couples from marrying and overturning the laws in five states where the institution is legal.

The presidential candidates reiterated their support for such an amendment during Monday night's GOP debate in New Hampshire.

Bachmann appeared to give a contradictory response – simultaneously saying she supports a state's right to make such decisions, then adding she supports altering the U.S. Constitution.

“I do believe in the 10th amendment and I do believe in self-determination for the states,” she said, then later added that she doesn't “see that it's the role of a president to go into states and interfere with their state laws.”

“I do support a constitutional amendment on marriage between a man and [a] woman,” she said, “but I would not be going into the sates to overturn their state law.”

Two candidates – former Godfather's Pizza CEO Herman Cain and Texas Rep. Ron Paul – said they do not back such an amendment. However, both men have previously said they oppose marriage equality. Cain recently said he believes being gay is a “sin” and a choice.

Santorum, possibly the GOP candidate who has received the most criticism over his opposition to gay rights, argued that a federal amendment takes state's rights into account.

“The constitutional amendment includes the states,” Santorum said. “Three-quarters of the states have to ratify it. So the states will be involved in this process. We should have one law with respect to marriage. There needs to be consistency as something as foundational as what marriage is.”