In anticipation of Senate votes this week on a proposed expansion of criminal background checks for firearms sales, one gun rights organization broke with the powerful National Rifle Association on Sunday to urge support for a compromise drafted by Sens. Joe Manchin III (D-W.Va.) and Patrick J. Toomey (R-Pa.).

The endorsement by the Citizens Committee for the Right to Keep and Bear Arms — which calls itself the second-largest gun rights organization in the country, behind the NRA, claiming 650,000 members and supporters — is one of several moves over the past few days that have provided a boost to the hopes of proponents of background checks.

While leading gun-control advocates — including President Obama and New York Mayor Michael R. Bloomberg (I) — back the bipartisan proposal, the announcement of support Sunday from the Citizens Committee reveals that substantial parts of the bill are viewed as “wins” for the gun lobby, including provisions that would prohibit a government registry of gun ownership and make it easier to transport and market weapons across state lines.

Though news of a split in the usually unified gun lobby cheered gun-control advocates, the gun lobby can count other probable wins in the current debate, such as the likely defeat of legislation to limit military-style assault weapons and high-capacity ammunition magazines. Now, an expansion of background-check requirements for gun sales is considered the most likely major achievement.

Initially, gun-control advocates hoped for a requirement for background checks of individuals purchasing a gun under most any circumstance. Currently, background checks are conducted only for purchases made from licensed gun dealers. The compromise measure, drafted by Toomey and Manchin, would require background checks for currently exempt online and gun-show sales but not for most other private transactions.

There were other signs of momentum on gun-control legislation over the weekend, including a tentative expression of support for the Toomey-Manchin compromise on Sunday from Sen. John McCain (R-Ariz.), an endorsement by Sen. Susan Collins (R-Maine), and indications of backing from several House Republicans, including some who have had previous endorsements from the NRA.

Officially, only three Republican senators — Toomey, Collins and Mark Kirk (Ill.) — have said they plan to vote for the Manchin-Toomey agreement. Democratic aides say the bill will need the backing of at least six Republican senators to pass. The measure still has a long and tortuous path, with dozens of amendments expected. The Senate is scheduled to begin formal debate Tuesday by first considering the plan to expand the gun background-check program.

Sixteen GOP senators voted late last week to proceed to debate, but several of them and some moderate Democratic senators said they are unlikely to support the bill’s proposed compromise amendments. It is not known how many amendments will be considered by the Senate over the next two weeks.

A decade ago, the NRA backed expanded background-check legislation, but it now stands firmly opposed. An NRA spokesman re­iterated the group’s opposition Sunday evening and again promised to score the Senate vote on the compromise in making future election endorsement decisions.

The group that backed the bill, the Citizens Committee, has far fewer members than the 4 million claimed by the NRA. It was founded in 1972 and functions as a kind of sister organization to the Second Amendment Foundation, a legal think tank and law firm based in Bellevue, Wash., that, along with the NRA, has been a leader in filing major court challenges to halt restrictions on gun rights.

“We decided to back it because we believe it is the right thing to do,” said Julianne Versnel, director of operations for the group.

The chairman of the Citizens Committee, Alan Gottlieb, told supporters in an e-mail Sunday that the group would embrace the Manchin-Toomey compromise. He urged members to read the senators’ proposal to understand why the gun rights group would back it.

Gottlieb made clear in his e-mail that he enthusiastically backs the bill the NRA opposes.

“If you read the Manchin-Toomey substitute amendment, you can see all the advances for our cause that it contains,” Gottlieb wrote. He then listed the gun rights advantages in the bill: “interstate sales of handguns, veteran gun rights restoration, travel with firearms protection, civil and criminal immunity lawsuit protection, and most important of all, the guarantee that people, including federal officers, will go to federal prison for up to 15 years if they attempt to use any gun sales records to set up a gun registry.”

These “advances” cannot be achieved, Gottlieb wrote, “unless we win the Senate vote on Tuesday to substitute Senators Manchin and Toomey’s balanced approach” to background checks. Gottlieb, like other gun group leaders, opposes a more far-reaching background-check bill proposed by Sen. Charles E. Schumer (D-N.Y.).

The organization has already been in touch with individual Senate offices. Some have already rejected its argument.

Sen. Tom Coburn (R-Okla.), who voted to proceed with debate, labeled the Manchin-Toomey agreement “unworkable and unfair to gun owners” in a message sent to constituents late last week. Because the plan would require gun purchasers to pay for a background check, “visitors to . . . gun shows across America will face a new tax of $30 to $50, and sometimes more, as they exercise their constitutional right to buy a gun,” Coburn said, adding that gun owners “will ignore and reject these changes.”

Other Republican senators who voted for debating the gun bill but plan to vote no on the amendment are Lamar Alexander (Tenn.), Bob Corker (Tenn.), Lindsey O. Graham (S.C.), John Hoeven (N.D.) and Johnny Isakson (Ga.), their spokesmen said Sunday.

Among Democratic senators, moderates Mark Begich (Alaska) and Mark Pryor (Ark.), who face difficult reelection fights in 2014, voted against proceeding with debate and are expected to oppose the overall gun bill. Max Baucus (Mont.), Kay Hagan (N.C.) and Mary Landrieu (La.), who are also facing difficult reelection prospects, voted for debate but have signaled they may vote against the Manchin-Toomey deal.

A Baucus spokesman said Sunday that the senator is reviewing the Manchin-Toomey proposal “and listening to feedback from Montanans to make sure they have a chance to weigh in.” A Landrieu spokeswoman noted that the senator voted to proceed to debate on the gun bill but hasn’t made up her mind on other amendments. Aides to Hagan did not respond Sunday.

Senate Majority Leader Harry M. Reid (D-Nev.) hopes to hold an up-or-down vote on the Manchin-Toomey plan by midweek and then proceed to vote on other amendments, according to senior Senate aides familiar with the plans.

Reid also is expected to call for a roll call on Democratic-backed amendments including the plan to ban military-style assault weapons, the aides said. A vote on the proposed ban, which is sponsored by 22 Senate Democrats, is expected to fall far short of the 60 votes needed to ensure final passage. Regardless, aides said Reid wants to hold a vote on the proposal early in the gun debate to fulfill his promise to Obama; the plan’s lead sponsor, Sen. Dianne Feinstein (D-Calif.); and gun-control groups that supported the ban.

Reid also hopes to hold a vote on a Democratic plan to limit the size of ammunition magazines, another proposal expected to fail, aides said. From there, he could proceed to a host of proposed amendments, including a bipartisan plan to provide more federal funding for mental health programs that assist military veterans, a Coburn proposal to establish an online portal for gun buyers to conduct their own background checks, a Republican plan to change the legal definition of mentally ill people when it comes to gun crimes, and an overarching GOP alternative to the underlying gun bill.

Gun-control advocates are worried about some of the expected amendments authored or backed by the NRA, including one that would provide a “national reciprocity” arrangement in which a gun owner who receives a permit to carry a concealed weapon in any one state would then be allowed to do that anywhere in the country.

Reps. Peter T. King (R-N.Y.) and Mike Thompson (D-Calif.) plan to introduce on Monday a House version of the Manchin-Toomey agreement that mirrors the bipartisan Senate deal. King, who represents a suburban Long Island district, said he hoped the Senate deal would extend background checks to include most private firearms transactions but that “there’s no sense of making the perfect the enemy of the good these days.”

“Rather than reinventing the wheel, we adopted Manchin’s plan because we thought that any bill that passes the Senate could pass the House,” King said in an interview Sunday.

Expanding the background-check program “is absolutely essential” to curbing gun-related violence in New York, King said, noting that most gun crimes in his state are committed with firearms illegally obtained in other states.

Only King and Thompson are sponsoring the bill, but other House Republicans who represent suburban districts in the Northeast and Midwest are expected to sign on if it advances in the Senate, King said. Separately, Republican House members from Pennsylvania with past NRA endorsements indicated support for the Toomey-Manchin approach, including Reps. Michael G. Fitzpatrick, Patrick Meehan and Charlie Dent.

In a sign of the wait-and-see attitude in the House, King said he has had no formal discussions with House GOP leadership or the House Judiciary Committee about his bill or when gun legislation will begin to move in the chamber.

Late Sunday, a second gun rights group, the Independent Firearm Owners Association, joined the Citizens Committee in endorsing the Manchin-Toomey proposal. The group is led by a former NRA regional political director, Richard Feldman, but has far fewer members than either of the more established gun rights groups.

Toomey said Sunday on CNN’s “State of the Union” that he expects a close vote this week on the measure. “I think it’s an open question as to whether or not we have the votes,” Toomey said. “I think it’s going to be close.”

Sean Sullivan contributed to this report.

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