WASHINGTON — Conservative senators from both parties announced their support for expanding background checks for gun buyers Wednesday, giving a burst of momentum to supporters of stronger restrictions. But big questions remain about whether President Barack Obama can push significant gun controls through Congress.

The compromise between Sens. Joe Manchin, D-W.Va., and Patrick Toomey, R-Pa., boosted the chances that the Senate will agree to broaden required background checks, a step gun-control groups laud as an effective way to keep weapons from criminals and the mentally ill. The senators are among the most conservative members of their parties, both have received “A” ratings from the National Rifle Association, 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 non-commercial 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, 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.”

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 today to begin debating Democrats’ gun legislation. That bill would also toughen laws against illicit firearms sales and provide a small increase in school security aid.

NRA spokesman Andrew Arulanandam said the organization opposes the Manchin-Toomey accord. The group said the focus should be on improving the nation’s mental health system and sources of violence like gangs.