Senate Finance Chairman Max Baucus (D-Mont.) and President Barack Obama worked furiously Wednesday to lure Republican Senate support for a health care overhaul, eyeing a self-imposed timeline that could force them to choose between bipartisanship and going it alone.

The Finance Committee was hoping to unveil a health care reform bill by week’s end that scores the support of most Democrats and a handful of Republicans. But Wednesday night that goal appeared increasingly elusive as Baucus continued to try to woo Republicans and Obama jumped into the ring by hosting key Republicans at the White House.

Baucus spent Wednesday huddling with GOP Finance members including ranking member Chuck Grassley (Iowa) while Obama hosted Republican Sens. Lisa Murkowski (Alaska), Bob Corker (Tenn.), Susan Collins (Maine) and Saxby Chambliss (Ga.).

Obama’s pitch to Republicans on health care comes during a week in which he had seemingly renewed his focus on bipartisanship. But at a Rose Garden event, the president seemed somewhat skeptical about whether Republicans will come aboard, indicating the effort would succeed only if GOP lawmakers “are serious about bipartisanship.—

As for Baucus, sources close to the Montana Democrat said that despite the ticking clock, he isn’t ready to throw up his hands. One senior source involved in the Finance talks said: “Discussions are continuing at a healthy pace, and real progress is happening in these meetings. Rather than focusing on timelines, it’s frankly worth focusing on the fact that several Members in the room expect to come up with a bipartisan agreement — and come up with it soon.—

As Baucus and Obama kicked up their lobbying campaigns, however, some Senate Democrats were starting to read the tea leaves, fearing GOP Senators would be an impossible get.

They suggested that Baucus — despite his months-long effort to craft a consensus bill — may not prevail and predicted Democrats ultimately would have to forgo bipartisanship.

“Sen. Baucus has been working extremely hard, and as effectively as anyone I’ve ever seen, to get the most Republican support,— said Sen. Debbie Stabenow (D-Mich.), a member of Finance. “But I think it will be predominantly Democrats [supporting the bill]. I think philosophically, we have a different way of viewing health care.—

Grassley, in a conference call with Iowa reporters Wednesday, said Democratic leaders may push Baucus to walk away from the talks, saying that if Baucus “is getting a lot of pressure from the White House, they may send a message, or Reid may send a message to him to just forget this bipartisanship stuff. We need to move ahead. Now, I hope that they don’t do that.—

The Senate Health, Education, Labor and Pensions Committee approved on a party-line vote its health care bill Wednesday. That measure is set to be merged with the Finance legislation, which had been set to be marked up sometime next week, and taken up as one vehicle on the Senate floor before the chamber adjourns on Aug. 7.

Sen. Orrin Hatch (Utah), who has been among the four Republicans Baucus is negotiating with, suggested that the push by Democratic leaders to meet Obama’s August deadline was as much to blame for obstructing a bipartisan deal in Finance as any lingering policy disagreements such as the role of the federal government or how to pay for the overhaul.

“How can there be?— Hatch said when asked if Finance is likely to produce a bill that has the support of more than one or two Republicans. “There are four of us on the Judiciary Committee in the Senate Sonia Sotomayor hearings. I mean, how can there be? I don’t even see how you can hold a mark up while we’ve got this kind of a responsibility — and I think it would be offensive if they tried to do that.—

Sen. Olympia Snowe of Maine, also one of the four GOP negotiators in Finance along with Grassley, Hatch and HELP ranking member Mike Enzi (Wyo.), is seen as the most likely target for Democrats to put a bipartisan stamp on the panel’s bill. But the moderate GOP Senator has also griped about the rush to pass a bill.

Although the continuing discussions in the Finance Committee are still being described as productive by Senators on both sides of the aisle, Obama early this week made it known that he wasn’t satisfied with the pace of legislative action. Baucus had originally intended to begin marking up his bill in late June, but he had pushed off that deadline as he continued to court a bipartisan deal.

In a meeting Monday at the White House with Baucus, Senate Majority Harry Reid (D-Nev.), Speaker Nancy Pelosi (D-Calif.) and key House Democratic committee chairmen, the president expressed his commitment to meeting the early August deadline to pass a bill out of each chamber and urged leaders to move more quickly.

Senate Democratic Conference Vice Chairman Charles Schumer (N.Y.) acknowledged Wednesday that the president’s new involvement has prompted panel members such as Sens. Kent Conrad (D-N.D.) and John Kerry (D-Mass.) to predict that a Finance markup would begin next week.

“The president, the first thing he did, more or less, when he came back was meet with the leadership of the Finance Committee— as well as Reid, Pelosi, House Majority Leader Steny Hoyer (D-Md.) and House Ways and Means Chairman Charlie Rangel (D-N.Y.) “and basically say, I will do whatever it takes to get this done.’ We have to get it done, he wants us to get it done … before the break,— Schumer told reporters. “And he galvanized things.—

But that pressure for speed has some Senators worried. Conrad, a key Finance negotiator and Senate Budget chairman, said he would prefer the emphasis be put on the quality of the health care legislation. Even Stabenow said it was more important to get the reform right than it was to meet the president’s deadline.

Obama has asked that legislation land on his desk no later than Oct. 15, and he has indicated that meeting that deadline could become difficult if the House and Senate fail to pass their separate bills before the break.

“Far more important than deadlines is getting this right,— Conrad said Wednesday after a meeting of Finance Committee Democrats.

Keith Koffler contributed to this report.