Watching President Obama’s bipartisan health-care summit, I was reminded of something George Bernard Shaw once said: “The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.”

The Republicans had clearly decided that it was in their best interest to act like the “unreasonable” men in the room—the more intractable, immoderate negotiators. They said the process should “start over from scratch,” as if there were enough time remaining before campaign season to repeat the entire ordeal, and they continued to characterize a market-based proposal to reform the private insurance industry as “a government takeover of health care.” Obama, meanwhile, sought advantage in seeming “reasonable,” making a show of shunning campaign rhetoric and insisting on finding specific areas where “both sides can work together.”

“I hope that this isn’t political theater, where we’re just playing to the cameras and criticizing each other,” Obama said at the start of the summit, “but instead are actually trying to solve the problem.” Seven hours later, he’d made no discernible progress.

This is the dynamic that largely defined Obama’s first year in office. So maybe it’s time to ask whether “reasonable” presidential leadership is an inherently flawed proposition. For many Americans the most appealing thing about candidate Obama was his rational cast of mind. After eight impractical, divisive years of George W. Bush, voters welcomed the prospect of a less ideological, more unifying presidency. Reason, the thinking went, would beget results that most people could get behind.

It hasn’t really worked out that way. In pushing for his biggest initiatives to date—the stimulus package and health-care reform—Obama has chosen to support what he believes to be the best possible proposal instead of what he believes to be the best imaginable proposal. His economic adviser, Christina Romer, initially recommend a $1.2 trillion stimulus bill, but when his chief of staff, Rahm Emanuel, said “it would be impossible to move legislation of that size” through Congress, Obama slashed the sticker price to $787 billion. Health care was more of the same. After calling himself “a proponent of a single-payer universal-health-care program“—and later advocating for a public option—the president wound up backing a private-market plan that’s nearly identical to the one that GOP leaders such as Bob Dole put forth in 1993.

Obama’s first year was hardly a failure. He passed legislation large and small and made far more progress on health-care reform than any of his predecessors had. But the results of his rationalism—a stimulus package that’s considered bloated on the right and insufficient on the left; a health-care bill that’s stalled in Congress, despite a commanding Democratic majority—have become deeply controversial. His approval rating, meanwhile, rarely cracks 50 percent, and his political capital is largely spent. “Obama won the election by being the rational, professorial type,” says Sean Wilentz, the liberal Princeton historian. “It’s still unclear, however, that what worked for him as a candidate can work for him as president.”

So the question is: would Obama be in better shape politically if he’d been a little less willing to adapt himself to the world, and a little more persistent in trying to adapt the world to himself?

A political theory called the Overton Window, named for the political scientist who developed it, hints at how a less reasonable approach to the presidency might have paid off. The term refers to the range of policies that the public can currently stomach. On health care, for example, a single-payer system is too far to the left, while an unregulated market is too far to the right. The Overton Window is somewhere in between. By promoting ideas that are meant to remain “unacceptable,” however, politicians can reposition the window. Prime the public with fringe proposals, the theory says, and eventually your target proposal will seem acceptable by comparison—even if it fell outside the Overton Window at the start of the process.

This technique worked for several of Obama’s predecessors, including the two most effective presidents of the last 100 years, Franklin D. Roosevelt and Ronald Reagan. Reagan promised to revolutionize Washington by simultaneously slashing taxes, trimming the bureaucracy, boosting defense spending, and erasing the budget deficit. But those around him knew that his proposals were unreasonable. Vice President George H.W. Bush had accused Reagan of peddling “voodoo economics” when running against him in the primaries, and Republican Senate Majority Leader Howard Baker compared supply-side policymaking to a “riverboat gamble.” But Reagan stood his ground, nudging the Overton Window rightward. When it came time to negotiate with Congress, a few tiny compromises—supporting a bipartisan budget bill and agreeing to a slightly smaller first-year tax cut—enabled Reagan to change the fiscal landscape in ways that would have seemed inconceivable only a few years earlier. He started with the ideal and settled for the possible, but only after changing what was possible in the process.

Roosevelt’s approach to creating Social Security was similar. He knew his timing was unreasonable. As NEWSWEEK’s Jonathan Alter writes in The Defining Moment: FDR’s Hundred Days and the Triumph of Hope, organized labor was lukewarm to the idea, and much of the Democratic Party, not to mention all of the GOP, was still fiscally conservative. But FDR was determined. He asserted his liberalism in mid-1935 with a flurry of legislation, including big tax increases for the wealthy. Social Security was the grand finale. Congress eventually sanded down FDR’s radical proposal, a process the president was happy to participate in. But the final bill—a delicate agreement between New Dealers and conservatives—was still far more liberal than anything that would have passed muster under Calvin Coolidge.

Likewise, a less reasonable approach might have helped Obama emerge from the health-care wars with more political capital, and more legislative victories, than he has now. His major mistake was starting the negotiations where he intended to end up, with a compromise bill at least as conservative as Richard Nixon’s 1974 proposal, and asking the Republicans to cooperate out of the good of their own hearts. There was never any political incentive for them to play ball. Passing the bill would make the president look like a bipartisan hero; blocking it would make him look like a failure. So of course the GOP angled for political advantage by calling Obama’s plan a communist plot to kill Grandma and resolving to oppose it at all costs, an “unreasonable” position that jerked the Overton Window rightward and left Obamacare looking radical when it was actually moderate.

But imagine that the president had tried to shift the Overton Window to the left by loudly advocating for a proposal that he knew would never pass, like the public option, which he supported in theory but refused to fight for, or even a single-payer system, which he rejected outright. The reaction would’ve been the same: the GOP still would’ve accused Obama of orchestrating a government takeover of health care, the tea partiers still would’ve showed up at town-hall meetings with shotguns. But at least he would’ve had some room to operate. Taking note of the (rather predictable) outrage on the right, Obama could have cut a deal with Republicans to eliminate all government involvement, either by dropping the public option or by replacing the single-payer system with private-insurance exchanges; he might have included tort reform in the package as well. Republicans would then have been able to claim that they reined in the president’s liberal ambitions and persuaded him to adopt conservative ideas. The Dems would have been disappointed, but they’d have signed on eventually. While Obama would have suffered a bit at first for seeming more radical than he actually is, he’d ultimately have earned points for his openness and bipartisanship. And the final legislation would have been a lot like the bill that Democrats are currently cobbling together in Congress, only it would’ve materialized much, much sooner, long before the country had had time to tire of the issue.

It’s impossible to say whether any Republicans would have cooperated with Obama in this alternate universe. But that’s not really the point. The electorate would have been far more amenable to Obama’s revised proposal, meaning that moderate House and Senate Democrats would’ve been far more comfortable supporting it, and Senate Republicans far more reluctant to filibuster.

Conservative New York Times columnist Ross Douthat recently referenced rumors that the White House had created a limited “fallback option” that would “insure half as many people as the House and Senate bills—15 million, all told—at a quarter of the cost.” He sounded grateful. “There’s a lot that you can do on insurance expansion for a quarter of the cost,” he wrote, “and given the fiscal situation now and going forward, that seems like a much better path to take.”

But what if single-payer or a strong public option had been the White House’s opening salvo and the current bill had been its fallback option. In other words, what if the Overton Window had started off further to the left? In that case, it’s not difficult to imagine conservatives like Douthat applauding Obamacare as it now stands. It’s not that Obama should be more liberal; it’s that acting more liberal at first could make him a more effective moderate. As the president prepares to wrangle with Congress over jobs, he might consider adding a little unreasonableness to his arsenal. Who knows? He might actually make some progress.