Georgia’s Republican U.S. Senators bucked an effort by conservative members of their caucus to block debate on gun-control legislation, allowing an opening for a bill that could expand the nation’s background-check system for gun purchases.

Sens. Johnny Isakson and Saxby Chambliss in statements Tuesday did not indicate how they would vote on the final bill, as key senators continue to negotiate a background-check compromise. In addition, Republicans will have a second chance at a filibuster.

But Isakson and Chambliss refused to halt the bill in its tracks, as more than a dozen senators – including Minority Leader Mitch McConnell of Kentucky – had threatened to do.

“I think it deserves a vote up or down,” Isakson said during an appearance on “CBS This Morning.”

The Senate has moved bills out of committee with bipartisan support that would increase funding for school security and step up penalties for “straw purchasing” of guns for criminals. Those are likely to be combined with an expansion of the national background-check system.

The Democrats’ preferred background-check proposal has drawn flak from the National Rifle Association and Republicans for being too onerous on transactions between friends, for example. Critics also have raised concerns about whether transaction record-keeping would lead to a federal gun registry, even though that is specifically prohibited by law.

Gun-control advocates have long sought to close the so-called gun show loophole in which background checks are not required for transactions that aren’t made through a licensed gun dealer. U.S. Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa., have been in talks this week on a compromise that could win both parties’ support.

“The issue on background checks now is how far they go and whether or not they violate rights to privacy in terms of mental health,” Isakson said on CBS. “I’ve just got to see the language they finally come up with to see what it does.”

Said Chambliss spokeswoman Bronwyn Lance Chester, “He does not support the underlying committee bill, but he thinks a full debate on the issue will be healthy.”

Chambliss and Isakson could prove to be key votes to clearing the bill’s first procedural hurdle, as only a handful of Republicans had committed Tuesday to supporting what’s known as a motion to proceed. From there, amendments can be added to the bill. Senate Majority Leader Harry Reid has said he would allow amendment votes to ban certain military-style weapons and large magazines, but they are almost certain to fail.

Once amended, the bill would again need to clear a 60-vote hurdle to end debate, a McConnell spokesman said. Isakson and Chambliss have not pledged their support at that critical juncture.

Gun advocacy groups see the motion-to-proceed vote — which is likely Thursday — as a critical moment, and Isakson’s and Chambliss’ stances are drawing criticism.

The filibuster to block debate was launched by U.S. Sens. Rand Paul, R-Ky., Ted Cruz, R-Texas, and Mike Lee, R-Utah, and grabbed support from several of the Senate’s staunchest conservatives.

Patrick Parsons, executive director of the Kennesaw-based Georgia Gun Owners, said his group has 10,000 paid members and a 130,000 email list in the state, and members have been pressuring the senators to join the filibuster.

“Things are black and white on guns, and this is a black-and-white issue,” Parsons said. “If they get past this filibuster, it’s bad news for gun owners.”

The lobbying has come from both directions, as gun-control advocacy groups step up their efforts in concert with the White House. On Tuesday Isakson met with family members of at least one victim of the December elementary school massacre in Newtown, Conn., which prompted the new focus on gun control in Congress.

President Barack Obama spoke in Connecticut on Monday, then brought several victims’ relatives to Washington on Air Force One. They had breakfast Tuesday with Vice President Joseph Biden before heading to Capitol Hill to plead with their representatives.

Tuesday afternoon Biden spoke to about 150 law enforcement officers, including Atlanta Police Chief George Turner and others from Georgia, about the importance of pushing an expansion of background checks. He raised his voice when denouncing senators vowing to block the gun bill: “What are they thinking?”

After the Biden event Norcross Police Chief Warren Summers said in an interview that universal background checks would help his department better trace guns used in crimes and block criminals from getting them in the first place.

“We’ve got to stop being Republicans and Democrats and be Americans,” Summers said. “We’ve got to take the guns out of the criminals’ hands, and that’s what I’m here for.”