Among the changes they might consider are limiting the fees buyers would pay at gun shows, adding provisions dealing with the mentally ill and altering language extending the background check requirement to all online sales, senators said Tuesday.
Supporters fell five votes short when the Senate defeated legislation last month that would have extended required federal background checks to more buyers.
That vote, four months after the massacre of 20 first-graders and six educators at a school in Newtown, Conn., was a defeat for President Barack Obama and gun control advocates. Senate Majority Leader Harry Reid, D-Nev., has promised to revisit the issue, perhaps by early summer.
Gun control groups have stepped up advertising, attendance at lawmakers' town hall meetings and other forms of pressure in an effort to convince at least five senators that they risk electoral defeat unless they reverse themselves and back the effort.
Once senators make that political calculation, many lawmakers and lobbyists believe the legislation would have to be changed so those senators could justify switching their earlier vote.
"Clearly this bill is going to have to look differently to allow members to face their constituents and explain why they changed their mind," said Sen. Chris Murphy, D-Conn.
"This is a pretty common-sense bill. I don't know how you make it any more common sense, except redefine some areas," said Sen. Joe Manchin, D-W.Va., who wrote the measure with Sen. Patrick Toomey, R-Pa.
The National Rifle Association said it was launching $25,000 in TV commercials in Manchester, N.H., on Wednesday defending the "no" vote by Sen. Kelly Ayotte, R-N.H. That ad says Ayotte protected "New Hampshire values" by supporting a GOP alternative that focused more on mental health and better enforcing current laws.
It is a response to TV commercials that criticizing her and which were financed by Mayors Against Illegal Guns, which is funded largely by New York City Mayor Michael Bloomberg. Those ads started running this week in Manchester and Boston in a buy exceeding $500,000, the group said.
Several senators who voted no have said they would consider revised versions of the legislation. None have committed themselves to changing their vote, and several have said they won't do so.
"I'm not changing my vote. I think we ought to move on," Sen. Johnny Isakson, R-Ga., one of the lawmakers gun control advocates have discussed trying to sway, said this week.
The defeated legislation would extend the background check requirement to include all transactions at gun shows and online. Transactions between relatives and other unadvertised sales would be exempt.
Background checks are currently required only for transactions handled by licensed gun dealers. The system is aimed at preventing criminals, the mentally ill and others from getting weapons.
Manchin told reporters he was considering changing the bill's language on Internet sales and how it treats family members, but was not specific. Sen. Jeff Flake, R-Ariz., has said he opposed the measure because its definition of commercial sales was too broad and could affect transactions between relatives.
Murphy said senators would support "a more robust portion of the bill dedicated to mental health" but provided no detail. Ayotte has said she wants a stronger effort aimed at the mentally ill, plus other changes.
Murphy said other possible provisions might address buyers who live far from gun dealers, where the checks are performed, and capping the fees charged for transactions at gun shows. Currently, there are no limits on fees gun dealers charge for some transactions that include background checks, which can range from roughly $20 to $100.
Gun rights advocates were also taking the offensive. Sen. Tom Coburn, R-Okla., prepared two gun-related amendments to a water infrastructure bill, and the Senate planned to vote on them Wednesday.
One would require federal agencies to report annually how many firearms and how much ammunition they have, exempting the Defense Department and the CIA. The other would allow firearms on an Army Corps of Engineers water resources facility if it didn't conflict with state law.
A pair of reports out Tuesday showed that gun violence has declined significantly over the past two decades.
A study by the government's Bureau of Justice Statistics found that gun-related homicides dropped from a peak of 18,253 in 1993 to 11,101 in 2011, down by over one-third. A report by the private Pew Research Center said gun homicides per 100,000 people fell from 7 in 1993 to 3.6 in 2010, a drop of nearly half.
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