Now that Democrats have lost their 60-vote, filibuster-proof majority in the Senate, Republicans have some ideas for how their stalled health overhaul can get started again: Find some bipartisanship.

“I don’t know one Republican who does not want health care reform. I don’t know one Republican who would not try to work together with the Democrats,” said Sen. Orrin Hatch, a Republican from Utah, on CNN’s Late Edition on Sunday. But, warned Hatch, “We would have to start over. There are a lot of things we can agree on right off the bat.”

Over on NBC’s Meet the Press, Senate Minority Leader Mitch McConnell of Kentucky picked up right where Hatch left off. “You start with junk lawsuits against doctors and hospitals, interstate competition among insurance companies,” he said.

But there’s a problem with that, says Len Nichols, who heads the health policy program at the nonpartisan New America Foundation. If you take most of the ideas that Republicans are shopping around at the moment, “then we’re back to a policy that frankly was rejected by the Republicans when they had a majority.”

Medical malpractice is a good example. Republicans have long advocated for a bill that would cap so-called noneconomic damages – those for victims’ pain and suffering – at $250,000. It passed the Republican-led House eight times between 1995 and 2005. But it never even won a majority in the Republican-controlled Senate, despite several attempts. Republicans have long blamed the failure on the influence of trial lawyers, but Nichols says there’s also just a lack of consensus on the issue.

“What’s interesting on malpractice is that a number of states have different models, which some states are very happy with,” he says. “And what President Bush and now what President Obama have both proposed – and what’s now in the legislation – is to encourage states to innovate along those lines.”

But it’s also important, Nichols says, for federal officials to “recognize that states are the place where medical malpractice jurisdiction lies, and therefore it’s better to have local medical communities in the states work this out.”

Another favorite Republican proposal is the idea of selling insurance policies across state lines. That would let people in one state buy cheaper insurance in another state. But without nationwide insurance regulations and a ban on insurers discriminating against people with pre-existing health conditions, the insurance might not cover as much. The idea also has alarmed state insurance regulators, who would no longer know who would be in charge of regulating what.

In fact, the idea has been so controversial, says Dave Kendall, of the centrist Democratic think tank Third Way, that Sen. Mike Enzi, a Republican from Wyoming, failed to get members of his own party to go along with it.

Enzi was one of the Republicans who spent much of last spring and summer unsuccessfully working to craft a bipartisan bill with Senate Finance Committee Chairman Max Baucus, a Democrat from Montana.

All of which makes Kendall wonder why Democrats would take Republican offers to work together any more seriously now.

“We had an opportunity to approach this in a bipartisan way, and Republicans made it very clear they were interested in taking down the president by defeating health care reform,” Kendall said. “So I don’t think it’s a real offer.”

Nichols, who says he was “for bipartisanship in health care before bipartisanship was cool,” says he’s frustrated at how polarized the sides have become. Particularly because the bill now stalled is fundamentally not that liberal.

He says both the House- and Senate-passed bills have far more in common with the bill put forward by Republicans in 1993 than with the competing plan pressed by then-President Clinton and congressional Democrats.

“Because it relies much more on markets, much more on individual requirements, much more on incentives in the health care system,” Nichols says. “And to claim that this bill is somehow a left-wing government takeover is rhetoric of a rather extreme sort, no question about it.”

In fact, Nichols says he finds it odd that Republicans have turned so strongly against the concept that underlies the Democrats’ bills – that of requiring everyone to have insurance. That’s because the so-called individual mandate began as a Republican idea of the early 1990s, “created back in the day as competition to the employer-mandate focus of Democrats at the time.”

At least for now, Democrats aren’t buying what Republicans are selling.

Asked Sunday on CNN about potential GOP cooperation, Sen. Robert Menendez, a Democrat from New Jersey, said: “When we hear about slow down and start over, it really means don’t do anything. Republicans have come to the conclusion that the president’s failure not only in health care but across the board is their way to political victory.”