Sen. Tom Coburn, R-Okla., doesn’t believe the gun violence legislation that Senate Majority Leader Harry Reid plans to bring to the floor early next month has a chance to become law without significant changes.

“I don’t think so — not at 60 votes, and if it does pass the Senate, it certainly won’t pass the House,” Coburn said, referencing the number of votes needed to beat back a filibuster.

Coburn opposes specific background check provisions that the Nevada Democrat has decided to include in the package.

Coburn said one of his concerns is increased costs associated with gun show transactions under the system.

“We’re going to raise the cost of purchasing at a gun show?” Coburn said in an interview for C-SPAN’s “Newsmakers” program. “A lot of the gun control people would love to see that happen, but it won’t be effective because if there’s a true portal out there, all they’ll do is make an agreement that I’m not buying … the gun here at this gun show.”

Despite his criticism of the specific Senate package, Coburn predicted that a background check measure that requires instant criminal background checks through a computerized portal would have broad support. He worked with several Democrats, including Sens. Charles E. Schumer of New York and Joe Manchin III of West Virginia, on a more substantive background check measure than is currently available, but the two parties were unable to reach a consensus on paperwork requirements. Schumer continues his effort to produce a bipartisan agreement with at least one other Republican.

“I don’t know a Republican that doesn’t want to have significantly enhanced and universal background checks. How you do that and protect the Second Amendment at the same time is very important, and we were very, very close,” Coburn said. He added that gun rights groups are concerned that the requirement to maintain records of the background checks could create a guilty-until-proven innocent situation long after the transaction is completed if a gun is later used in a crime.

“They wanted you to be able to prove in the future that you did that, he said.

The problem with the record keeping, in Coburn’s view, is that it would “put at risk gun owners who actually followed the law and 11 years later can’t find a piece of paper that said they did it right.”

Reid’s move to include the criminal background check language with robust record keeping in the Senate bill won accolades from some supporters of more stringent gun control, though that may not help the effort to secure the 60 votes that would be needed to break a filibuster.

“I applaud Sen. Reid for sending a bill to the Senate floor that includes comprehensive, enforceable background checks and for emphasizing that to be effective, any bill that passes the Senate must include background checks,” New York Mayor Michael Bloomberg said in a statement. “This sensible reform — with overwhelming support from Americans, including gun owners — will save lives and keep our communities safer.”

In the C-SPAN interview that will air Sunday, Coburn disagreed with the idea that a majority would back more background checks paired with requirements that sellers keep a paper trail for gun purchases.

Concerns on Immigration Overhaul

Coburn also expressed concerns with the immigration overhaul discussions under way, saying that he remains unconvinced about border security, which he thinks should be solidified before having a broad discussion about establishing a pathway to citizenship.

“You are never going to get the votes until you can demonstrate and certify that we have secured our borders,” Coburn said.

He added that he has traveled to some more remote parts of the U.S.-Mexico border where security is still weak. He suggested further enhancements to fencing, technology and intelligence are needed to crack down on illegal border crossings.

“The point is — is we can control our border. We have chosen not to yet,” he said.

Asked about what sort of concrete requirements he would have for determining the border is secure, Coburn deferred to the judgement of fellow members of Congress for certifications.

“Congress would make that decision every year. Are we maintaining the border? Have we controlled the border? Have we done what we what we need to do?” Coburn said. “And I don’t even want to talk about the rest of it until we do that, because people in this country aren’t worried about immigration, they’re worried about illegal immigration.”

Fellow Republican Sen. Rand Paul of Kentucky said earlier this week that he also would like to see annual Congressional votes on the extent of border security efforts. Paul has displayed an openness to supporting a broader immigration overhaul that includes a way for people currently without legal status within the United States to eventually attain citizenship.