A new federal plan by two senators may reflect what many people have already been thinking: background checks for more gun buyers.

Some conservatives who are wary of changing gun laws are OK with increased background checks, including certified firearms instructor Richard Finke of Albert Lea.

“Background checks are fine,” Finke said. “What they’re doing right now, they’re doing a good job.”

A bipartisan U.S. Senate proposal to expand background checks for gun buyers gained the backing of one Republican and the potential support of a second Sunday as sponsors said the vote expected this week was too close to call.

The plan would “strengthen the background check system without in any way infringing on Second Amendment rights,” Maine Sen. Susan Collins said in a statement explaining her support for the measure. But she added that “it is impossible to predict at this point” what will be in a final bill.

Arizona Sen. John McCain, who has a B-plus rating from the National Rifle Association, said he was “very favorably disposed” to the proposal that has emerged from Sens. Patrick Toomey, R-Pa., and Joe Manchin, D-W.Va.

“I appreciate their work,” McCain said. “And the American people want to do what we can to prevent these tragedies. And there’s a lot more that needs to be done, particularly in the area of mental health.”

It was in McCain’s home state that a gunman with schizophrenia shot then-Rep. Gabrielle Giffords in the head during a 2011 rampage in Tucson that left six people killed.

Collins and Sen. Mark Kirk of Illinois are the only two Republicans besides Toomey who are expected to vote for the compromise as of now.

It will take 60 votes to pass, meaning that more Republicans will have to come on board because some Democrats from gun-friendly states are expected to oppose the measure.

“It’s an open question as to whether or not we have the votes. I think it’s going to be close,” Toomey said.

The measure requires background checks for people buying guns at gun shows and online. Background checks currently apply only to transactions handled by the country’s 55,000 licensed gun dealers. Private transactions, such as a sale of a gun between family members, would still be exempt.

Manchin urged lawmakers to read the 49-page proposal. He said it should dispel any misconceptions about infringing on the constitutional right to bear arms.

“I think universal background checks should be done,” Austin Police Chief Krueger said months ago in the midst of widespread gun debate. Krueger noted a loophole for large gun shows, where anyone can purchase guns and not have to go through a background check.

Mower County Sheriff Terese Amazi is onboard with more background checks and said there are flaws with the current system.

“I think we do have issues we’re trying to do our permits to carry and our permits to purchase,” she said.

Amazi noted discrepancies in documentation for some people who have no apparent restrictions from owning firearms but are federally prohibited. Furthermore, she said people actively going through court cases can create confusion, too.

Subjecting more firearms purchases to federal background checks has been the chief goal of Obama and gun control supporters, who promote the system as a way to prevent criminals and other potentially dangerous people from getting the weapons.

The senators said their plan would help keep firearms from criminals and mentally ill.

Even so, the ultimate fate of gun legislation remains unclear, clouded by opposition from the National Rifle Association and many Republicans and moderate Democrats in the Democratic-led Senate and the Republican-run House. Many critics say the effort would violate the Second Amendment right to bear arms and burden law-abiding gun owners.

While Finke is OK with improved background checks, he fears the move is the first step in taking away some of those Second Amendment rights.

“It’s a smaller step, but it’s only the first step,” Finke said. “Once they get that, they’ll go after some more.”

Finke thinks legislators should shift the focus to better mental health evaluation and care in the U.S.

In a written statement, the NRA was critical of the proposed legislation.

“Expanding background checks at gun shows will not prevent the next shooting, will not solve violent crime and will not keep our kids safe in schools,” it said. It added policymakers should focus on fixing the country’s mental health system and on gang violence.

“President Obama should be as committed to dealing with the gang problem that is tormenting honest people in his hometown as he is to blaming law-abiding gun owners for the acts of psychopathic murderers,” the NRA said.

Currently, the background check system covers sales only by licensed gun dealers. The compromise would apply the system to all commercial sales, such as transactions at gun shows and online. The sales would have to be channeled through licensed firearms dealers, who would have to keep records of the transactions.

Yet Finke added online sales must already go through a licensed dealer, so there is no issue there.

Private transactions that are not for profit, such as those between relatives, would be exempt from background checks, the proposal says.

Sen. Chuck Schumer, D-N.Y., who led an earlier unsuccessful effort to strike a bipartisan background check deal, is backing the compromise after changes were made from an initial version of the deal by the two senators.

The overall gun bill also tightens federal laws against illegal gun sales and slightly increases federal aid for school safety.

“People should listen to what we have to say and move the debate forward,” said Mark Barden, who lost his 7-year-old son, Daniel. “It’s not just about our tragedy. Lots of kids are killed every day in this nation. We have to help lead the change.”

Few supporters of the legislation are confident of victory, though. Several weeks of emotional, unpredictable Senate debate lie ahead, and a mix of gun-rights amendments, opposition from the National Rifle Association and skepticism from House Republican leaders leave questions about what will emerge from Congress. Foes of the proposed new restrictions say they would penalize law-abiding citizens and do nothing to curb gun violence.

— The Associated Press contributed to this report.