"One of the fundamental questions is, do you try to do reform all in one bill for one seventh of the economy or do you do it in stages?" Butler said. "I think American public have said they want to see it in stages. Republicans could be drawn in on the idea of doing this in stages ... and make that commitment."
Lawmakers also need to address the question of how much flexibility to give states, many of whom are already fighting back against the Democrats' health care proposals.
Virginia this month passed a law prohibiting a requirement for residents to purchase health care insurance and other states are looking to follow suit with similar bills.
"I think that a package that would help states expand coverage in different ways, in different places, is something" that would get broad political support, Butler said.
Some Republicans, such as Rep. Paul Ryan, R-Wis., are suggesting ways to change the tax treatment of health coverage. Even though the idea hasn't gained traction among most Democrats yet, Obama has praised Ryan for putting serious ideas on the table that he is willing to consider.
Overwhelmingly, experts say Republicans need to be more specific about their ideas.
"I don't think Republicans have clear a vision as the administration and the Democratic leaders and party," Butler said. "It's because they're not in power."
Reinhardt pointed out that even among themselves, Republicans have too many different ideas and at least three different proposals on the table, some of which are right along the lines of what Democrats are already saying. Sen. Tom Coburn's, R-Okla., bill, for example, is highly regulatory, Reinhardt said.
"Eighty percent of what Coburn wants is in the [Senate] Democratic health care bill," he said. "And they seem not to have a vision."
At the same time, Reinhardt said the Democrats' bill has "a lot of garbage in it."
Still, what the White House should say, argued Reinhardt, is that the Democrats have "worked out a proposal that at least has the benefits of being washed out by some political process. Only Democrats were voting, but at least it has had some washing."
Despite the administration's hopes of bipartisanship, many doubt whether the public wrangling over health care is merely for show or if there is a genuine push toward reform.
"My hope is that this doesn't end up being political theater, as I think some of you have phrased it," the president told reporters Tuesday. "I want a substantive discussion."
Nevertheless -- whether the president likes it or not -- health care has become a case of political posturing, Baker said.
"I think President Obama really lost control of the process early on when he made the decision that he would drop it in Congress's lap," he said. "[Now] he's paying a price for it."
Experts agree that the president has to take back control of the health care push, and more importantly, convey it to the public in simple terms.
Even though a majority of Americans now disapprove of the way Obama is handling four out of five major issues -- the economy, creating jobs, health care and the deficit -- an astounding 63 percent said lawmakers in Washington should keep trying to pass a comprehensive health care reform plan, rather than giving up on it, according to the latest ABC News/Washington Post poll.