President Barack Obama and Health and Human Services Secretary Kathleen Sebelius discuss health care reform Thursday in Washington, D.C.

Washington ? With Republicans apparently unmoved by a daylong face-off on live TV, President Barack Obama and Democrats in Congress face the test of whether they can overhaul the nation’s health care system by themselves.

Obama conceded Thursday after seven hours of sometimes testy talks with Republicans that the two parties may be too far apart on the biggest health care issue: whether the federal government should pay for insurance for tens of millions of people who don’t now have coverage.

He urged Republicans one last time to consider any hope of agreement. Barring that, however, he signaled that Democrats will press ahead, perhaps using a controversial rule to get legislation through the Senate with a simple majority rather than the usual 60-vote supermajority that they can’t assemble without at least one Republican.

Even then, he and Democrats face significant challenges in mustering enough Democratic votes in the House of Representatives. Democrats suggested that they have a few more weeks to pass health care legislation before they take a spring recess and turn to other issues.

“I’d like the Republicans to do a little soul-searching and find out are there some things that you’d be willing to embrace that get to this core problem of 30 million people without health insurance,” Obama said at the conclusion of the daylong session at the Blair House, across from the White House.

With his quest for universal health care stalled in Congress, Obama had convened the extraordinary, televised session with top aides and 38 members of Congress from both parties. The president and his team made their case anew for a nearly $1 trillion, 10-year plan to expand health insurance to millions of the uninsured, improve coverage for those who do have insurance and control costs for everyone who pays insurance premiums.

Republicans countered with a scaled-down plan, arguing for a slower, step-by-step approach. “We believe that our views represent the views of a great number of the American people, who have tried to say in every way they know how — through town meetings, through surveys, through elections in Virginia and New Jersey and Massachusetts — that they oppose the health care bill that passed the Senate on Christmas Eve,” said Sen. Lamar Alexander, R-Tenn.