WASHINGTON - Casting health-care overhaul as a legacy to benefit the American people and failure as politically unthinkable, President Obama yesterday rallied Senate Democrats to deliver on their party's half-century quest to expand the social safety net to include access for all.

At the Capitol during a rare Sunday session of the Senate, Obama delivered a closed-door pep talk, lasting about 45 minutes, to the fractious Democratic caucus.

Sen. Frank Lautenberg (D., N.J.) said senators were moved to "deep reflection, and even some tears."

"He talked about how this would be a legacy, that each of us could look back to having been part of, 10 or 20 years from now," said Sen. Kent Conrad (D., N.D.), a fiscal conservative. "All the things that we hope to achieve are - at least in part - in this package."

Deep divisions remain in the party over abortion coverage, but there was hope for compromise on whether the government should offer health insurance in competition with private companies.

"They're going to get it done," Obama said as he left. He avoided specifics in the meeting with senators and took no questions.

The health-care legislation - Obama's signature domestic policy goal - would provide coverage to more than 30 million additional people over the next decade with a new requirement for nearly everyone to purchase insurance.

There would be a new marketplace where people could shop for and compare insurance plans, and lower-income people would get subsidies to help them afford coverage.

The federal-state Medicaid program for the poor would be expanded, and there would be a ban on unpopular insurance company practices such as denying coverage based on medical history.

Senate Majority Leader Harry Reid (D., Nev.), who had invited Obama, sounded confident. Republicans "want this to be, as one senator said, President Obama's Waterloo," Reid told reporters. "And it's not going to be."

Democrats are keenly aware of former President Bill Clinton's failure to pass health-care legislation in 1994, and their repudiation at the polls that November.

Obama said this is "the most significant social legislation in decades - so don't lose it," said Sen. Joe Lieberman (I., Conn.). Obama was accompanied by Vice President Biden and other senior administration officials.

Obama "pledged to work with us in any meaningful way that he can," Reid told reporters.

Republicans, nearly unanimous in opposing the bill, said Democratic senators were under political pressure.

"The Democrats are trying to squeeze every one of their members to swallow a very bitter pill for the American people," the GOP's Senate leader, Mitch McConnell of Kentucky, said.

Reid has 58 Democrats and two independents in the Democratic caucus. He may be able to get one or two Republican votes, at the most. He is still short of the 60 votes he needs to shut off debate and move to a final up-or-down vote on the bill.

At Reid's request, moderate and liberal lawmakers are trying to find a compromise on the government insurance plan that they could all support and that could also potentially attract Sen. Olympia Snowe of Maine, the one Republican to vote for the Democrats' health overhaul bill in committee.

A new idea under discussion involves national nonprofit insurance plans that would be administered by the Office of Personnel Management, which oversees the popular Federal Employees Health Benefits Program.

Snowe called the possible compromise "a positive development."