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Still, about a dozen Republican senators, including Minority Leader Mitch McConnell of Kentucky, have said they will work to block the motion to proceed on the legislation, preventing it from getting to the floor for debate. On Tuesday, Mr. McConnell cited the dearth of Republican votes for the legislation in committee as the reason for joining the fight.

Talks also continued Tuesday between Sens. Joe Manchin III, West Virginia Democrat, and Patrick J. Toomey, Pennsylvania Republican, on background checks — the current centerpiece of the package. The two senators have scheduled a news conference for Wednesday at 11 a.m.

Mr. Reid said he hopes something will work out between those two and Mr. Kirk, and that he would like to see their product be one of the first amendments offered to the bill passed out of the Senate Judiciary Committee.

Mr. Manchin said Tuesday evening that he’s “very hopeful” about reaching a compromise Wednesday.

“Let me say that these have been all good talks — they really have been,” he said.

But Sen. Chuck Grassley, Iowa Republican and ranking member of the Judiciary Committee, said Mr. Reid is forcing the Senate “to take a leap into the unknown” and that “we are being asked to vote to proceed to an uncertain bill.”

“The world’s greatest deliberative body should not operate in this fashion,” he said.

Nevertheless, Mr. Reid has pledged to move forward — even if the vote fails.

If the package does not get the 60 votes needed to move to the floor, he plans to offer pieces of gun legislation, like the weapons and magazine bans, as well as background checks, one by one.

That move would fulfill Mr. Obama’s call for his proposals to receive votes and force Republicans to oppose each of them individually, but would likely do nothing to move any of them closer to actual passage.

And regardless of what happens in the Senate, any bill would face an even more hostile environment in the House, where the Republican leaders who control the chamber have said only that they would look at whatever the Senate passes.

It’s unclear whether the current background check language, as written, could obtain the 60 Senate votes needed. The senators are trying to expand the types of sales and transactions that would be subject to background checks without angering gun rights advocates, who fear universal checks could give way to a national registry.

Federally licensed firearms dealers are required to conduct background checks, but private sellers and dealers at gun shows are exempt.

Sen. Mike Lee, Utah Republican, is one of those planning to filibuster the motion to proceed. He said claims by President Obama and Democrats that Republicans are trying to block the debate are misleading.

“The president again is trying to rush legislation through Congress because he knows that as Americans begin to find out what is in the bill, they will oppose it,” Mr. Lee said. “Our job in Congress is to do everything in our power to ensure the public understands these bills and how it affects their rights as citizens.”