Manchin told reporters the compromise on background checks would be the first amendment offered when the Senate begins debating the package of gun legislation.
Senate Majority Leader Harry Reid, D-Nevada, said Tuesday he would hold a vote on opening debate on the gun package Thursday, putting pressure on Manchin and Toomey to finalize their agreement intended to overcome a Republican filibuster of the legislation.
The filibuster pledged by 14 GOP senators means Reid, whose Democratic caucus holds 55 seats, needs 60 votes to open debate on the gun legislation.
Democrats believe that as many as a dozen GOP senators will vote with them, making up for the handful of pro-gun Democrats who might vote against launching debate on the bill.
Obama has made gun measures a major focus of his second-term agenda, holding events across the country to push for Congress to vote on the package.
He spoke Monday in Connecticut, where the Newtown shootings occurred, and Vice President Joe Biden made a similar call for action at the White House on Tuesday.
A successful GOP filibuster would prevent a vote on specific components of the legislative package. Even if an amended bill passes the Senate, approval from the Republican-led House remains uncertain.
House Speaker John Boehner, R-Ohio, was noncommittal on Wednesday on prospects for gun legislation, telling reporters he would wait to see what the Senate passes.
Meanwhile, Democratic Rep. Mike Thompson of California and Republican Rep. Peter King of New York said they planned to introduce legislation in the House similar to the Senate compromise by Manchin and Toomey.
Obama's rhetoric has reflected the political uncertainty, with the president and his aides using increasingly personal language intended to shame Republicans into allowing public votes on measures that have public support but are fiercely opposed by the NRA.
On the other side, the NRA and its supporters in Congress say the Democratic proposals threaten the constitutional right to bear arms, and also offer ineffective responses intended as political show instead of real solutions to the problem of gun violence in America.
"On firearms questions, on Second Amendment questions, there's a divide in this country," NRA President David Keene told CNN. "To call it an ideological divide is too simple because it's a cultural divide. When something happens, the folks on the other side from us say, 'well the problem's the gun, we need to do something about guns.' "
Failing to pass new gun laws would be a stinging defeat for Obama and Democrats.
However, a public perception that Republicans blocked popular proposals, such as expanding background checks, could harm GOP prospects in 2014 and 2016 among moderates they need in their corner to have any chance of countering strong support for Democrats by minority demographics such as Hispanic Americans, African Americans and the gay-lesbian vote.
A new national survey showed that 86% of Americans support some expansion of background checks.
At the same time, the CNN/ORC International poll released Wednesday also showed a majority of respondents fear that increased background checks would lead to a federal registry of gun owners that could allow the government to take away legally owned weapons.
Keene and other opponents worry that an expanded background check system would create a paper trail that could eventually be used to build a national gun registry, which they reject as unconstitutional.
They also contend it would prove a burden to law-abiding gun owners while doing nothing to stop criminals from getting hold of firearms.
"The one thing you know today is that if the government creates a record, it's not secure," Keene said, adding that requiring background checks on all gun sales -- the so-called universal system -- raised the question of "is it linked to a national registration scheme."
According to a summary of the compromise proposal, it includes language that prohibits creation of a national gun registry or misusing information from background checks.
The high political stakes of the divisive gun law debate have bred hardball tactics and strategies.
The NRA has long kept a comprehensive scorecard of the voting records of legislators on gun issues, which it combines with campaign contributions to try to influence elections.
In response, a group led by New York Mayor Michael Bloomberg called Mayors Against Illegal Guns announced this week it was launching its own scorecard to identify members of Congress who vote against tougher gun laws.
The Senate Judiciary Committee passed a package of gun laws proposed by Obama after the Newtown attack by a lone gunman.
Proposals in the committee's package included expanding background checks on gun buyers, toughening laws against gun trafficking and straw purchases, banning semiautomatic rifles modeled after military assault weapons as well as large-capacity ammunition magazines, and coming up with ideas for improving school safety.