Are voters ready to move on?

Editor's note: David Gergen is a senior political analyst for CNN and has been an adviser to four presidents. A graduate of Harvard Law School, he is a professor of public service and director of the Center for Public Leadership at Harvard University's Kennedy School of Government. Follow him on Twitter.

(CNN) -- With the Supreme Court's thunderbolt, a crucial battle is over on health care, but the war surely goes on. Or does it?

There has been a widespread view among conservatives that if the court were to uphold Obamacare that would do more to galvanize the tea party and other parts of their base than any other outcome. Anger and frustration can be powerful motivators in politics.

On cue, Mitt Romney immediately seized upon the court's decision to whip up Republican voters, arguing that now the only way to replace Obamacare is to replace President Obama. House Republicans are promising a quick, symbolic vote to overturn the law after July Fourth. And conservative groups are preparing to pour in millions of dollars in ads against the Patient Protection and Affordable Care Act that will begin hitting as early as Friday.

David Gergen

Opinion: Health care victory, but still a long way to go

Clearly, the war moves to a new front as far as the right is concerned. And in truth, the GOP should be able to mobilize a higher turnout from its base this November.

But the base alone will not be enough to win: The GOP also needs to draw in boatloads more of moderate and centrist voters. And whether those folks are going to welcome new rounds of fighting over the health care law remains to be seen.

My hunch is that a sizable number will think the war over health care has gone on long enough, and they will want to move on to more important issues. Jobs and deficits have long been trumping health care around most dinner tables.

Obama: It's a victory for the people

Romney: I'll do what justices didn't

How will the court's ruling affect you?

Short-term loss for conservatives?

For better or worse, the court struggle came to be seen as the decisive battleground in trying to repeal the health reform law. Partisans on both sides, along with the press, created an expectation that the court would strike down the mandate, the keystone in the arch. Obama would be shown as another ineffectual Jimmy Carter, losing much of his authority.

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But now that the court has spoken definitively on behalf of Obama -- and even Chief Justice John Roberts sided with the president -- there is likely to be a sense that the dam has broken. Especially among those who have been ambivalent about health care reform legislation -- and there are millions who like portions of it even though they don't much like it overall -- psychology may change. "Time to give it a rest; let's get our focus back to the economy."

How the public responds to the health care decision over the next couple of weeks will be critical. This is a moment when tides could shift.

Obama was smart in his reaction to the court: He didn't gloat too much over his huge victory, and he left open the door to alterations in the law in the months ahead. After some weeks of stumbling, he seemed presidential.

Romney is riding a tiger: To stay on top, he must continue to give voice to the tea party -- and if he falls off, as the joke goes, they will eat him. But a series of strident attacks against Obama and his health care plan will not be enough. To win, he must also reach voters beyond his base, showing that he understands their concerns and will speak for them, too.

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Overheard on CNN.com: Health care law a 'necessary evil'

The opinions expressed in this commentary are solely those of David Gergen.