Those moderate Democrats include Nelson, Arkansas Democrats Sen. Blanche Lincoln and Sen. Mark Pryor, Delaware Sen. Thomas Carper and Louisiana Sen. Mary Landrieu. The liberal Democrats include Wisconsin Sen. Russ Feingold, Iowa Sen. Tom Harkin, Ohio Sen. Sherrod Brown, West Virginia Sen. Jay Rockefeller and New York Sen. Chuck Schumer.
The president's appearance signals Democrats' urgency to pass health care legislation before the end of the year, as well as the difficulty of the task.
At least two major sticking points remain on reaching the votes they need; the controversial public option and abortion services.
"Thanks to Senator Harry Reid's leadership, we're down to two major issues, abortion and public option. And I think we're coming to closure on those issues. We're likely to come to a vote on the abortion question maybe by tomorrow," Sen. Richard Durbin said on "Fox News Sunday."
A new alternative to the public option was put forth Saturday that could satisfy fiscally conservative Democrats who're opposed to the public option, such as Sen. Evan Bayh, D-Ind., or for whom voting for the controversial measure would be politically risky, such as Lincoln of Arkansas.
The new alternative would essentially offer Americans a national health plan similar to the one that federal employees receive. The new plan would be administered by the Office of Personnel Management, which already runs the Federal Employee Health Benefits Plan that provides members of Congress and federal employees low-cost insurance.
Only not-for-profit insurance options would be offered in the new plan.
"There has to be an approach that either creates a new public option or an expansion of current public programs," Sen. Feingold said Sunday on ABC's "This Week." "We have to have some competition for the insurance industry."
That proposal is gaining some interest from senators who have said they would support a Republican filibuster unless the public option is stripped from the bill that Senators have been debating on the Senate floor.
"I'll feel more comfortable when its out," said Sen. Joe Lieberman, a Connecticut independent who caucuses with Democrats. "I don't understand exactly what's in this new proposal so I want to see it if its private and there's no federal government financial exposure and the government is not creating an insurance company, well that's one way."
But the proposal is still in its planning stages and must be fleshed out. That could further delay the floor debate as Democrats try to meet the latest in a series of self-imposed deadlines, passing a bill through the Senate this year.
Internal disagreements about the public option reflect a wide gap in the Democratic Party. Some, such as Sen. Arlen Specter of Pennsylvania, support a more robust public option plan.
"It isn't a single payer [system] and it is not going to add to the deficit. It's going to be a level playing field," the former Republican said at a joint news conference with Sen. Susan Collins, R-Maine, and Lieberman. "I would invite everyone to read the fine print."
Asked whether his final vote will be determined on the public option, Specter said, "I'm not going to make any concessions ... on a strong public option."
Sen. Ron Wyden, D-Ore., said on ABC's "Top Line" Thursday that the public option as structured in the Senate health care bill would result in a pool insuring only the unhealthiest, unless it's available to all Americans.