Debate on a major overhaul of the of the nation’s gun-control laws is scheduled to begin Tuesday in the U.S. Senate, but there were still not enough votes late Monday to assure expansion of the national gun background check program for gun sales, which is the centerpiece of the proposal.

The debate will focus on a bipartisan proposal to expand the national gun background check program to include virtually all commercial gun sales.

Uncertainty over the fate of the proposal, in the form of an amendment to the underlying gun bill, came as the National Rifle Association and other gun-rights proponents intensified their efforts to defeat the measure by warning that even some of the elements in the plan that are supposed to be “pro-gun” could undermine Second Amendment rights.

The primary authors of the amendment, Sens. Joe Manchin III (D-W.Va.) and Patrick Toomey (R-Pa.) spent most of Monday lobbying wavering colleagues with phone calls, letters, discreet in-person meetings and personal deliveries, as Manchin deployed his office interns Monday afternoon to distribute copies of the proposal to each senator’s office.

“What we’re talking about is not creating any new laws, we’re talking about uniforming the laws that we have,” Manchin said in afternoon speech on the Senate floor.

In an effort to win the support of some undecided rural-state senators, Manchin and Toomey were discussing the possibility Monday of adding language that would exempt select far-flung communities in Alaska and North Dakota from some background check requirements, according to Senate aides familiar with the talks. Such exceptions could help win the support of Alaska’s senators Mark Begich (D) and Lisa Murkowski (R) and North Dakota Democrat Heidi Heitkamp, a moderate with an A-rating from the NRA.

The amendment will require at least 60 votes to clear Senate procedural rules and ensure final passage, but it still lacks sufficient support, based on an analysis by The Washington Post. The votes of just 22 of 100 senators are in play, including the 16 Republicans who voted last week to proceed with debate on the gun bill and six moderate Democrats who face difficult reelections in 2014 or represent rural states with strong gun cultures and would face strong political pressure at home for supporting new gun-control legislation.

Among the Republicans, at least nine said said Monday that they plan to vote against the Manchin-Toomey deal: Lamar Alexander (Tenn.), Saxby Chambliss (Ga.), Tom Coburn (Okla.), Bob Corker (Tenn.), Jeff Flake (Ariz.), Lindsey O. Graham (S.C.), John Hoeven (N.D.), Johnny Isakson (Ga.) and Roger Wicker (Miss.).

Isakson’s decision is especially disappointing to gun-control groups, who hoped he would vote in favor of the plan after supporting similar proposals when he served in the Georgia state legislature.

Among the six Democrats, Sen. Kay Hagan (N.C.) announced Monday that she will vote for the plan. Spokesmen for the five other Democrats — Max Baucus (Mont.), Begich, Heitkamp, Mary Landrieu (La.) and Mark Pryor (Ark.) — said Monday that the senators were reviewing the proposal and soliciting input from constituents before making a decision.

Another potential complication for Democrats is the ailing Sen. Frank Lautenberg (D-N.J.), who has been absent because of illness for most of the year. Democrats have mostly excluded Lautenberg’s vote from potential whip counts and have said privately that they will work to bring him back to Washington only if his support is absolutely needed.

But amid growing pressure to explain his absence, Lautenberg spokeswoman Caley Gray said Monday that “Senator Lautenberg is feeling better and hopes to be in Washington for gun votes this week.”

Among the undecided, the lobbying has been intense. Gun-rights and gun-control groups pursued an inside and outside game Monday on Capitol Hill as lobbyists for both sides huddled during the day, examining the possibilities of wooing one legislator or another to their side.

At one point Monday morning, proponents of the compromise measure thought the count was so close that they recommended a delay in the planned vote, according to people familiar with the talks. But Democratic aides said they remained confident that the proposal would eventually have sufficient support for passage.

In the hope of encouraging other senators to oppose the plan, the NRA turned to academics whose research has been funded in part by the group. David Kopel, a Second Amendment expert with the Colorado-based Independence Institute, a legal think tank that receives NRA funding, said the Manchin-Toomey plan includes “empty phrases for purposes of mollifying the most credulous gun owners.”

In a blog post circulated by the NRA, Kopel wrote Monday that the compromise contains “a bonanza of gun control.” He said he was concerned that the Senate compromise bill contained language that could inadvertently support creation of a government list of gun owners, an oft-cited concern of those who fear government confiscation of weapons. Kopel said the language also suggests that promised new rights for those transporting weapons across state lines could actually result in greater penalties for gun owners in some jurisdictions.

Supporters of the measure rejected those arguments. At the White House, Vice President Biden hosted a conference call with gun-control advocates, and said that “The NRA has done a — not very good, but relatively good job at disinformation out there.” He added, “The NRA is now trying to scare the heck out of people.

“The black helicopter crowd thinks that, you know, we’re going to swoop down and steal their guns,” Biden said, dismissing such theories.

Biden said he thinks there is momentum to overhaul the nation’s gun laws.

Meanwhile, advertising and social media campaigns urged supporters to call Capitol Hill on Monday. There were emotional demonstrations, too.

The mother of a gun violence survivor from Virginia Tech presented 1.3 million signatures on petitions on Capitol Hill advocating “common sense gun control measures.” The parent of the shooting victim, Lori Haas, planned to deliver the petitions as part of a broader campaign organized by The effort is directed at undecided moderate Democrats.

Philip Rucker contributed to this report.

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