WASHINGTON (USA TODAY) -- Senate Majority Leader Harry Reid said the Senate will "hit pause" on the gun bill while senators see if they can find a workable compromise on strengthening background checks on gun purchases.

Reid, D-Nev., said he consulted with President Obama and agreed "the best way to pass a background check bill is to hit pause," which will "allow senators to keep negotiating."

One possible way forward: A broader exemption for rural areas that would allow those who don't live near a federally licensed dealer to buy guns at gun shows or over the Internet without a background check.

"There are ways to create broader exceptions," said Sen. Chris Murphy, D-Conn., a champion of stricter gun control after 26 people -- including 20 children -- were shot and killed at Sandy Hook Elementary School in Newtown, Conn., last December. "We are going back to the table on that issue."

In dropping the gun bill, Reid moved onto a measure to require Internet retailers to collect state sales taxes. But he pledged that "we're going to come back to this bill,"and even outlined a number of amendments that will get votes.

Republicans won't oppose coming back to the gun issue.The No. 2 Republican in the Senate said Thursday that the defeat of the Manchin-Toomey background check compromise shouldn't prevent Congress from passing a gun bill.

Senate Minority Whip John Cornyn, R-Texas, said he hoped Democrats "would not choose to quit." He said the Senate could still do more to improve the federal background check system -- especially in adding mental health and drug abuse records.

Reid said Thursday's action would allow the Senate to come back to guns without having to "start at square one" after the Senate adopted two amendments Thursday:

• An amendment on privacy, sponsored by Sen. John Barrasso, R-Wyo. The amendment would withhold 5% of a state's community-oriented policing grant money if it publicly releases gun ownership information, except as part of law enforcement or court proceedings. That amendment was adopted, 67-30, far exceeding the 60-vote threshold after red-state Democrats crossed over to vote with Republicans.

• The Mental Health Awareness and Improvement Act, sponsored by Sen. Tom Harkin, D-Iowa. The measure supports and encourages school violence prevention efforts, suicide prevention and mental health awareness. The amendment doesn't yet have any funding behind it, and had broad bipartisan support. The vote was 95-2, with only Sens. Mike Lee, R-Utah, and Rand Paul, R-Ky., voting no.

But the underlying bill, as it exists, cannot pass in its current form because it contains background check requirements even more strict than the compromise blocked in a 54-46 vote Wednesday.

In a speech on the Senate floor, Cornyn delivered the most complete GOP response to Wednesday's defeat of the Manchin-Toomey compromise, which would have expanded background checks to sales at gun shows and over the Internet.

Cornyn accused the president of taking the "low road" by blaming the National Rifle Association's influence.

"It's absolutely false to say it comes down to politics," Cornyn said.

"I'm not worried about the gun lobby," he said. "I don't work for them. I work for 26 million Texans. ... The views I represent in the United States Senate are their views. I'm accountable to them, and no one else."

Cornyn said he's explained his reasoning personally to families of Newtown shooting victims. The measures Obama called for, he told them, would "celebrate symbolism over solutions" and would not have prevented the Dec. 14 massacre.

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