(CNN) - Nonpartisan political handicapper Stuart Rothenberg said Sunday it's hard to imagine Republicans can run entirely on a platform against Obamacare from now until the November midterm elections.
"I think the cake has been baked on the (Affordable Care Act)," Rothenberg said on CNN's "State of the Union." "I don't think there are a bunch of people changing their opinions now."
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He acknowledged that campaigns in the past have gone big on a simple message – e.g. "It's the economy, stupid" from Bill Clinton's 1992 presidential campaign - but he said Republicans will need to do more this cycle than just train their fire against Obamacare.
"That's a fine message, (but) they've got to talk about growth and jobs, and what the President does or has not done," he added.
Sean Spicer, the communications director for the Republican National Committee, indicated on the same program that Republicans have no plans to back away from their main line of attack.
"It's clear that Obamacare is still the No. 1, No. 2, and No. 3 issue going into this election," he told CNN chief political correspondent Candy Crowley. He pointed to Democrats who are running in competitive Senate races - most of them in red or purple states - who have made blatant efforts to distance themselves from the health care law.
Republicans also cite the recent special House election in Florida, won by the Republican nominee, who focused largely on attacking Obamacare.
But President Barack Obama is telling his party not to give up. In announcing last week that 8 million Americans had signed up for insurance through the marketplaces, he called on Democrats to "forcefully defend and be proud" of the law.
"I don't think we should apologize for it. I don't think we should be defensive about it. I think there is a strong, good, right story to tell," Obama told reporters Thursday.
While that may be good advice for Democrats running in solidly Democratic districts or states, it's a "dangerous game" for Democrats running in places that are less blue, said Rothenberg, who's the editor and publisher of the Rothenberg Political Report.
"They're trying to really finesse the race where they're running as independent Democrats, not national Democrats," he said, adding that "talking about the President's premiere national accomplishment" may not be the best strategy.
Mo Elleithee, communications director for the Democratic National Committee, argued that Republicans are going to hurt themselves by maintaining the battle to repeal Obamacare.
"The one thing that is much more unpopular than the Affordable Care Act is repealing the Affordable Care Act," Elleithee said on CNN. "And people are tired of the fight."
The Republican-controlled House has voted at least 50 times to undo or alter the health care law. That's a record that Democrats highlight when defending the ACA. They say that while the law needs some improvements, making those fixes is better than repealing the law entirely.
"The repeal debate is and should be over," Obama said last week.
But what does the polling really say?
Most nonpartisan surveys still show that more Americans oppose the new health care law than support it.
However, when asked about repealing or replacing Obamacare, Americans are more split on the issue. An ABC News/Washington Post poll released last month showed 49% opposed Republican efforts to replace the new health care law, while 47% supported them.
A separate Pew Research Center survey in March indicated that among those who disapprove of the law (53% of adults nationwide), 30% said they believe elected officials should do what they can to make the law work as well as it can, while 19% said they should try to make the law fail.