But he conceded, "There's no panacea here."
Expanded background checks are at the core of the Democratic gun control drive. Other top proposals - including bans on assault weapons and high-capacity ammunition magazines - will be offered as amendments during Senate debate but seem destined for defeat.
The compromise between Toomey and Manchin, both owners of guns who have "A" ratings from the NRA, was likely to improve the prospects that the Senate might expand background checks by attracting broader support. But debate could last weeks, and it was not known what amendments to the overall bill, either constricting or expanding gun rights, senators might approve.
Neither Toomey nor Manchin predicted the Senate would approve gun legislation, and each said his vote on final passage would depend on what the measure looked like when debate ends. Manchin said he would vote against the overall legislation if his compromise with Toomey was defeated.
Reid said the first amendment will be to add the Manchin-Toomey compromise to the legislation.
The senators' agreement also has language expanding firearms rights. That includes easing some restrictions on transporting guns across state lines, protecting sellers from lawsuits if buyers passed a check but later used a firearm in a crime and letting gun dealers conduct business in states where they don't live.
Underscoring the difficult path gun curbs face in the GOP-run House, Speaker John Boehner, R-Ohio, repeated his plan to wait for the Senate to produce something and pointedly noted that the background check agreement had yet to pass Senate muster.
"It's one thing for two members to come to some agreement. It doesn't substitute the will for the other 98 members," he told reporters.
Said Toomey: "Criminals and the dangerously mentally ill shouldn't have guns. I don't know anyone who disagrees with that premise." He said expanding the checks wasn't gun control, "just common sense."
Background checks currently apply only to transactions handled by the country's 55,000 licensed gun dealers. Advocates of expanding the system say too many sales - the exact proportion is unknown - escape the checks, which are supposed to keep weapons from going to criminals, the seriously mentally ill, and others.
In a written statement, Obama said, "This is not my bill," adding that he wished the agreement was stronger. Still, he praised it as significant progress, saying, "We don't have to agree on everything to know that we've got to do something to stem the tide of gun violence."
Gun control groups gave the deal warm but not effusive praise, noting that unknown details and some pro-gun provisions gave them pause.
The NRA said it opposed the agreement.
And in a letter to senators, NRA lobbyist Chris W. Cox warned that the organization would include lawmakers' votes on the Manchin-Toomey deal and other amendments it opposes in the candidate ratings it sends to its members and supporters.