Sixty-eight senators, pressured by the families of those killed in gun violence, came together last week to overcome a filibuster threat that would have quashed the debate on a broader gun bill. But many of those votes are clearly not translating into yes votes for the only background check measure that has attracted bipartisan support.

“We’ve got some work to do,” Mr. Manchin said in an interview Sunday. “You’ve got some very close Democratic colleagues who are having some difficulties, and our Republican colleagues are trying to get comfortable.”

On Sunday, a small gun rights group, the Citizens Committee for the Right to Keep and Bear Arms, came out in favor of the Toomey-Manchin amendment, prompting Mr. Manchin to say he hoped the endorsement would help win more yes votes. Also on Sunday, Senator John McCain, Republican of Arizona, said he was inclined to support the measure; his vote, should it be yes, could bring along others and push the bill toward the 60 votes needed for final passage. .

And supporters of gun safety legislation, including President Obama, plan to campaign all week to win over some lawmakers who have expressed misgivings. Public pressure to pass gun legislation is also intensifying, with the families of the people killed in the Newtown, Conn., school massacre last year waging a highly public, and potent, campaign to win over lawmakers.

But an accounting of likely votes shows how difficult it could be to pass new gun legislation.

Senator Mark Begich, Democrat of Alaska, says he will vote against the measure, and at least three other Democrats are expected to join him in trying to defeat it, including Heidi Heitkamp, a freshman senator from North Dakota. Some left-leaning Democrats may also balk because of the gun-rights provisions that have been added to the bill to entice Republicans.