"I think President Obama will have to work very, very aggressively ... [and] be prepared to pull out all the stops. That's the most likely path," Baker said. "If he could basically shame some of the more moderate Republicans such as [Maine Sen.] Olympia Snowe into coming on board in a public session and try to put them on the line, I think that might be a way he gets bipartisanship."
Sen. Judd Gregg, the top Republican on the Senate Budget Committee, has also been billed as another GOP leader who has shows signs of bipartisanship on the health care front. But the senator from New Hampshire is also calling for the administration and lawmakers to start from scratch.
"I say, let's step back, let's start with a blank sheet of paper. And let's start putting on that sheet of paper things we can agree about," Gregg said in an MSNBC interview Friday.
Baker said he is "not terribly optimistic" about the summit at the end of this month. However, there are areas where Republicans and Democrats can come together and coalesce on a new bill.
Obama has said he wants to see specific proposals from Republicans on what health care reform should entail.
"I think that what I want to do," Obama told CBS News' Katie Couric in an interview on Feb. 7, "is to look at the Republican ideas that are out there and I want to be very specific: How do you guys want to lower costs? How do you guys intend to reform the insurance markets so people with pre-existing conditions, for example, can get health care? How do you want to make sure that the 30 million people who don't have health insurance can get it? What are your ideas, specifically?"
Republicans have, for the most part, opposed major Democratic proposals -- an option of a government-run health insurance plan that would compete with the private sector, taxes on high-end "Cadillac" plans, Medicare cuts and taxes on the wealthy, among a laundry list of other features.
But experts say the two parties can find common ground and work piecemeal to come up with a bipartisan solution to the health care crisis facing the country.
Both parties have said they want to get rid of pre-existing conditions clauses that prevent many Americans from obtaining health insurance.
The difference between the two schools of thought is that some, including Obama, say that doing so without making insurance mandatory would result in people exploiting the system. Those who are healthy would only get insurance when they need to, which wouldn't be cost efficient.
Others argue that the government cannot dictate whether Americans should be required to have health insurance and that a mandate isn't necessary. Those proponents say that the federal employee health care program has been successful and it does not mandate insurance.
The other area where bipartisanship can be achieved is on SCHIP -- State Children's Health Insurance Program. The program designed to cover uninsured children has received support from both sides of the political aisle. The original legislation was sponsored by Democratic Sen. Kennedy and Sen. Orrin Hatch, R-Utah, in 1997.
Outside of specific legislation, experts say leaders of the two parties need to decide how to move forward with health care.