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“I can’t understand why allowing a few thousand gay American citizens to sponsor their partners for legal immigration is more objectionable than granting amnesty to millions of illegal immigrants,” he said.

White House spokesman Jay Carney said the president’s interest is to make sure the Senate doesn’t squander “a unique opportunity” to reform the nation’s immigration system.

“There are obviously a lot of amendments that will be considered,” Mr. Carney said. “We urge every senator as he or she considers this legislation to understand that no one can get everything they want out of this process.”

Mr. Leahy has not said whether he will demand a vote on his amendment. He withheld his proposal when the bill was before the Judiciary Committee, because adding it in there almost certainly would have scuttled the legislation.

Lengthy debate

The gay-rights amendment is one of about 100 amendments filed in the first 48 hours of the immigration debate.

The Senate held its first vote on amendments Thursday and rejected a Republican proposal for stiffer border security standards.

As written, the bill grants legal status to illegal immigrants in six months, but withholds a full pathway to citizenship for at least a decade while the government takes steps to improve security along the border with Mexico.

But Sen. Chuck Grassley, Iowa Republican, said enhanced border security should come even before legalization. Mr. Grassley said tying the two together is the only way to make sure the government follows through on its security promises.

“Border security first, like promised,” Mr. Grassley said.

Sen. Charles E. Schumer, New York Democrat and one of the bill’s chief authors, said putting security first would ruin the bill. He argued that full security would take too long and leave illegal immigrants in limbo.

“What do we do for five, six years until the border is fully secure? It’s going to take awhile to do it. We need to bring equipment there, we need to build fences there,” he said.

Mr. Grassley’s amendment was defeated on a 57-43 vote.

Stephen Dinan contributed to this report.