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WASHINGTON — President Barack Obama is paying a rare weekend visit to Capitol Hill to urge Senate Democrats forward as they work through the weekend to try to resolve their differences on his sweeping health care overhaul.

The president’s planned appearance at a Senate Democratic caucus meeting Sunday afternoon answers appeals from a number of lawmakers eager for him to step in and help Senate Majority Leader Harry Reid finish the job in pushing forward his top domestic policy priority.

“The president is going to come in and urge us to bring this ball across the line, to finish this, as he should. This is an historic opportunity,” said Illinois Sen. Richard Durbin, the No. 2 Senate Democrat.

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Sen. John Cornyn, a Texas Republican, viewed Obama’s closed-door visit with Democrats differently.

“I regret that the president is going to continue what has been a partisan approach to health care reform,” Cornyn said. “Obviously, the president and Senate Democrats have made a decision to do it their way without accepting input from Republicans.”

Obama and Reid must unite liberals and moderates in the 60-member caucus in the face of near-solid Republican opposition, even as moderates balk over abortion and a proposal for the government to sell health insurance in competition with the private market. Sixty is the precise number needed to overcome Republican stalling tactics in the 100-member Senate, so Reid doesn’t have a vote to spare.

“I think if we don’t deliver, we’ve got a problem,” said Sen. Dianne Feinstein of California, when asked on a Sunday talk show about the political consquences for Democrats should they fail to produce a bill.

Moderate and liberal lawmakers met throughout the day Saturday to try to find a compromise on the government insurance plan, or public option, 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.

Republican Sen. Jon Kyl of Arizona, the second-ranking Senate Republican leader, said that right now his party remained united against the Democratic bill, which he complained would “get the government very deeply involved into health care at an enormous expense.”

A new idea being discussed was national nonprofit insurance plans that would be administered by the Office of Personnel Management, which oversees the well-liked Federal Employees Health Benefits Program.

Sen. Blanche Lincoln of Arkansas, a key centrist Democrat, was enthusiastic about the idea, which she’s proposed in different forms in the past. “I think it bodes well for being able to do what we want to do, which is to create greater choice and options in the marketplace,” she said.

Liberal Democratic senators were cool to the proposal, holding out for a fully government-run plan.

“I’m willing to talk to anybody about anything but they haven’t sold it yet,” said Sen. Sherrod Brown of Ohio. “We have compromised enough on the public option.”

Someone will have to give. But despite the apparent divide, lawmakers and White House officials sounded increasingly optimistic.

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“It’s going really well. They’re having a lot of really productive meetings,” Nancy-Ann DeParle, director of the White House Office of Health Reform, told reporters in the Capitol Saturday. “It’s about where it should be at this point in the legislative process.”

Reid called the unusual weekend sessions as he races to finish the sweeping bill by Christmas.

The nearly $1 trillion, 10-year legislation being debated in the Senate would provide coverage to more than 30 million uninsured Americans over the next decade with a new requirement for nearly everyone to purchase insurance. There would be new marketplaces 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 grow, and there would be a ban on unpopular insurance company practices such as pulling coverage when someone gets sick.

Tens of millions of Americans lack health insurance or are underinsured, either because their employers do not provide it or they are out of work. The United States is the only developed industrialized nation that does not have a comprehensive national health care plan.

The House of Representatives passed its version of health care reform legislation last month. Assuming the Senate passes some version of health care overhaul, a House-Senate conference committee would try to resolve the differences. Then both chambers would vote on the final product and, if they approve it, send it to Obama’s desk for signing.

Durbin and Cornyn spoke on “Fox News Sunday,” while Feinstein and Kyl were on CNN’s “State of the Union.”

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