Sen. Patrick Leahy on Tuesday introduced, but ultimately withdrew, an amendment that would have allowed gay and lesbian U.S. citizens to use the nation's immigration system to petition for their partners they married in other countries.

Leahy, a Democrat from Vermont, introduced the amendment as the Senate Judiciary Committee he chairs was debating a sweeping immigration bill that could legalize the nation's 11 million unauthorized immigrants while increasing border control and revamping the nation's legal immigration system.

Leahy wanted to use that bill as a way to change federal law so it recognizes marriages from other countries if the marriage "could have been entered into" in a U.S. state — same-sex marriage is legal in 12 U.S. states, including his own.

Republicans warned that including the amendment would sink the immigration bill. During Tuesday's debate, Sen. Lindsey Graham, R-S.C., said the "strong but fragile" coalition they've put together to pass immigration reform would collapse if Leahy the amendment was made part of the bill.

"If we try to define marriage within the immigration debate, it would mean the bill would fall apart because the coalition would fall apart," Graham said.

Democratic senators expressed their support of Leahy's amendment. Sen. Charles Schumer, D-N.Y., explained how he has been a co-sponsor of the Uniting American Families Act, or UAFA, for years. Sen. Dick Durbin, D-Ill., discussed his opposition to the Defense of Marriage Act, which affirms the power of states to decide whether to accept same-sex marriages in other states.

"I believe in my heart of hearts that what you're doing is the right and just thing," Durbin said. "But I believe this is the wrong moment, this is the wrong bill."

Leahy, "with a heavy heart," withdrew the amendment.

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