Florida Republican Sen. Marco Rubio, a co-author and key proponent of the Senate immigration bill, said he will revoke his support if an amendment is added that allows gay Americans to petition for same-sex spouses living abroad to secure a green card.

"If this bill has in it something that gives gay couples immigration rights and so forth, it kills the bill. I'm done," Rubio said Thursday during an interview on the Andrea Tantaros Show. "I'm off it, and I've said that repeatedly. I don't think that's going to happen and it shouldn't happen. This is already a difficult enough issue as it is."

The amendment, introduced by Vermont Democratic Sen. Patrick Leahy, would grant green cards to foreign partners of gay Americans. Leahy originally introduced the measure during the Senate Judiciary Committee markup of the bill, but he withdrew it under pressure from Republican lawmakers who said it would reduce the chance of the bill passing.

The effort underway in Congress to overhaul the nation's immigration system is a bipartisan one, and its success hinges on a fragile coalition of political, business and religious groups that span the ideological spectrum. Opponents of Leahy's amendment have said repeatedly that his proposal would cause some key groups to withdraw their support and kill the bill. Rubio's exit would be especially devastating to its survival.

The Senate is expected to vote on Leahy's amendment soon.

In the interview, Rubio also said that as the bill is currently written, it has "no chance" of passing.

"If the border situation is not improved in this bill, this bill won't pass," he said. "It won't pass the Senate and it has no chance in the House. It won't become a law and we're wasting our time."

This article has been updated to more accurately define Sen. Leahy's amendment.