In a separate interview on CBS, Manchin acknowledged the power of the NRA, saying: "They won't be with us on this and I just would hope that they would allow their members to see the facts and let them vote their conscience."
Both senators said Monday that part of the problem involves misconceptions about their compromise, and they urged colleagues to read the 49-page measure instead of relying on what they called erroneous political rhetoric by opponents.
Their amendment expands background checks to gun shows and all Internet sales, but exempts private transactions such as hunting rifles traded among family and friends.
It also makes it easier for hunters and sport shooters to transport their firearms across state lines. It would also require states and the federal government to provide records on criminals and the "violently mentally ill" to the national background check system, addressing a criticism by the NRA and other opponents of gun laws that the existing system lacks substantive information.
In addition, the plan calls for a new National Commission on Mass Violence to report in six months on "all aspects of the problem, including guns, school safety, mental health, and violent media or video games."
The NRA opposes the compromise as a possible first step toward a national gun registry and therefore a violation of the constitutional right to bear arms.
However, smaller pro-gun groups have come out in favor of the Manchin-Toomey amendment, indicating a rift in the gun lobby over the emotional issue of taking legislative action in response to the Newtown killings.
Manchin said Monday he was reaching out to senators who voted last week against beginning debate on guns.
"We're working on all of them. Some of them who might not have voted for cloture might be more receptive once they see the facts," he said. "Now that we have gun groups coming out in support, it really helps us."
Manchin and Toomey noted Monday that their proposal includes a specific prohibition against a national gun registry as well as criminal penalties for misusing background check information for that purpose.
In a statement on Sunday, moderate Republican Sen. Susan Collins of Maine said she would support the compromise because it exempted private family gun transactions from needing a background check, calling it a "commonsense approach" that required the screening only for commercial transactions.
Even if the compromise passes and the Senate proceeds to approve a broader gun package, it was unclear if the Republican-led House would go along.
House Speaker John Boehner, R-Ohio, has stopped short of promising a vote, saying only that the chamber would look at whatever the Senate sends over.
Obama has made the gun legislation a major focus of his second term, holding events across the country to push for congressional action and public pressure.
Last weekend, the mother of one of the Newtown schoolchildren killed in December delivered the weekly presidential address instead of Obama.
Francine Wheeler, whose 6-year-old son Ben died in the attack by a lone gunman, noted that since the December 14 killings, "thousands of other Americans have died at the end of a gun."
"Thousands of other families across the United States are also drowning in our grief," Wheeler said. "Please help us do something before our tragedy becomes your tragedy."
The issue has raised attention on overall gun deaths in the country, with supporters of tougher gun laws noting that more than half all homicides involve firearms and U.S. levels are higher than other countries.
On Saturday night, a man shot himself to death during a NASCAR event sponsored by the NRA in Texas.