A possible breakthrough legislative proposal on gun background checks was met with a mixed response ahead of a key test vote Thursday, with the White House giving its blessing while some top Republicans and gun rights groups still voiced concerns.

Senate Democrats plowed ahead with a planned test vote on the sweeping gun control legislation. The so-called cloture vote is set for 11 a.m. ET Thursday, and a congressional aide told Fox News that Democrats are likely to reach the 60-vote threshold needed to proceed toward debate and eventually a final vote. They will face resistance from more than a dozen Republican senators, including Sen. Rand Paul, R-Ky., who have vowed to try to block the legislation.

A compromise struck between conservative Sens. Joe Manchin, D-W.Va., and Patrick Toomey, R-Pa., boosted the legislation's chances and earned praise from President Obama.

"I applaud Senators Joe Manchin and Pat Toomey for their leadership on forging a bipartisan agreement around commonsense background checks that will make it harder for dangerous people to get their hands on a gun," Obama said in a written statement. "This is not my bill, and there are aspects of the agreement that I might prefer to be stronger. But the agreement does represent welcome and significant bipartisan progress."

But Sen. Tom Coburn, R-Okla., echoed many Republicans in calling it "a good-faith but unworkable plan."

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"The proposal will impose new taxes and unreasonable burdens on law-abiding citizens. The agreement also prioritizes collecting records over protecting citizens," Coburn said. "This is the wrong approach. Preventing sales to dangerous persons, not collecting receipts, will save lives."

The National Rifle Association followed up with its own criticism of the proposal.

"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," the NRA said. "The sad truth is that no background check would have prevented the tragedies in Newtown, Aurora or Tucson."

Other Republicans voiced concern that the legislation being voted on Thursday still included the older background check measure. Senate Republican Leader Mitch McConnell, who plans to vote against proceeding on Thursday, said that background check provision would be a "clear overreach."

"The following offenses would now be federal crimes absent surrendering their firearms and conducting a background check. Federal offenses: an uncle giving his nephew a hunting rifle for Christmas; a niece giving her aunt a handgun for protection; a cousin loaning another cousin his hunting rifle if the loan occurs just one day before the beginning of hunting season," he said.

The Manchin-Toomey plan would be voted on later as an amendment. Manchin and Toomey both have received "A" ratings from the NRA, and their endorsements could make it easier for hesitant colleagues to back the effort.

Gun control advocates still face opposition from many Republican senators and resistance from moderate Democrats, including several facing re-election next year in GOP-leaning states. In the Republican-run House, leaders have shown little enthusiasm for Obama's ideas, making that chamber an even higher hurdle.

Under the agreement the two senators announced at the Capitol, background checks would be expanded to all for-profit transactions including sales at gun shows and online, with records kept by licensed gun-dealers who would handle the paperwork. Exempted would be noncommercial transactions such as between relatives. Currently, the system applies only to sales by the country's 55,000 federally licensed firearms dealers.

The agreement also contains provisions expanding firearms rights, and that concerns gun control supporters. Some restrictions on transporting guns across state lines would be eased, sellers would be shielded from lawsuits if the buyer passed a check but later used a firearm in a crime and gun dealers could conduct business in states where they don't live.

"Truly the events at Newtown changed us all," said Manchin, citing the Connecticut town where December's murders of 20 first-graders and six educators propelled gun control to the top rank of national issues. "Americans on both sides of the debate can and must find common ground."

Emotion, always prominent in the gun issue, cropped up late Wednesday when Manchin met with relatives of the Newtown victims in his Senate office, telling them that "this will not be in vain." He became choked up when a reporter asked about the impact of the family members' visit, saying, "I'm a parent, a grandparent ... and I had to do something."

Said Toomey: "Criminals and the dangerously mentally ill shouldn't have guns. I don't know anyone who disagrees with that premise." He said that expanding the checks wasn't gun control, "just common sense."

The agreement makes it all but certain that the Senate will reject a conservative blockade and vote Thursday to begin debating Democrats' gun legislation. Besides broader background check requirements, the bill would also toughen laws against illicit firearms sales and provide a small increase in school security aid.

Underscoring that the fight was far from over, NRA spokesman Andrew Arulanandam said the organization opposes the Manchin-Toomey accord. The group, which has fought most of Obama's gun proposals and claims nearly 5 million members, said the focus should be on improving the nation's mental health system and sources of violence like gangs.

"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," the NRA said.

On a day when first lady Michelle Obama was visiting a violence-plagued high school in Chicago, the Obamas' hometown, the NRA said, "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."

House Speaker John Boehner, R-Ohio, repeated his view that the Senate should act, saying, "It's one thing for two members to come to some agreement. It doesn't substitute the will for the other 98 members."

In a written statement, Obama said he'd prefer stronger language than the compromise, but he said it represented progress.

"It recognizes that there are good people on both sides of this issue, and we don't have to agree on everything to know that we've got to do something to stem the tide of gun violence," he said.

Other highlights of Obama's gun agenda -- including bans on assault weapons and high-capacity ammunition magazines -- seem to have little chance of winning approval in the Senate, let alone the House.

Polls show more than 8 in 10 people back expanded background checks. Even so, the fight will be difficult in both chambers, especially the House, where increasing numbers of district lines are drawn to protect incumbents, said James Pasco, executive director of the Fraternal Order of Police.

"They're not going to have a constituency in every instance that is champing for that bill," said Pasco, whose group has backed the drive for expanded background checks.

The director of Mayors Against Illegal Guns, one of whose leaders is New York City Mayor Michael Bloomberg, said the compromise was a major improvement and showed that Republican support was possible.

"Opposing yet another reform, which has Americans scratching their heads, is not a place where a national political party can afford to be," said Mark Glaze.

Reflecting concerns about unseen details about some gun rights language, the Brady Campaign to Prevent Gun Violence took a more tempered view.

"While we continue to review the legislation, we believe a majority of the components are a good step forward," said Brian Malte, director of the campaign's network mobilization.

There are no current, definitive statistics on how many gun sales occur annually and what portion occurs without the checks. A study in the 1990s found that up to 40 percent of transactions involved no checks.

Fox News' Chad Pergram and the Associated Press contributed to this report.