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'kill' immigration bill

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CNN's Ashley Killough

(CNN) – Sen. Marco Rubio flatly stated Thursday that he'll vote against his own immigration bill if it ends up including rights for gay and lesbian couples.

"If this bill has in it something that gives gay couples immigration rights and so forth, it kills the bill. I'm gone. I'm off it," he said. "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."

Democratic Sen. Patrick Leahy of Vermont proposed such legislation this week, filing an amendment that would require the government to recognize same-sex marriages in which one spouse is an American.

"Seeking equal protection under our laws for the LGBT community is the right thing to do," Leahy said in a statement announcing the measure.

It's unclear whether the Senate will vote on the amendment, but the proposal virtually has no chance of winning the 60 votes almost certainly needed to clear the 100-member chamber.

The senator first proposed the legislation when the Senate Judiciary Committee marked up the bill last month. With vigorous opposition from some Republicans and some Democrats saying they wouldn't support the amendment, Leahy ultimately withheld his proposal.

Rubio, who made his comments Thursday on a conservative radio show hosted by Andrea Tantaros, also warned that he'd withdraw support from the bill if the final version lacks tougher border security provisions–a refrain he has consistently pushed in recent days.

"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. We're wasting our time."