Correction: An earlier version of this story had an incorrect title for Matt Canter, deputy executive director for the Democratic Senatorial Campaign Committee.

House Republicans haven’t given up on dismantling the Affordable Care Act, but their focus has changed. Jackie Kucinich looks at the GOP’s new approach that comes just in time for the midterm elections. (Theresa Poulson/The Washington Post)

Will the Affordable Care Act be the Republicans’ golden ticket in this year’s midterm election? Some worry that the GOP may be placing too big a bet on it.

Nearly every advertising dollar being spent against Democratic congressional candidates is going toward pounding them on the new health-care law.

That strategy could miss the mark, warned Louisiana Gov. Bobby Jindal, who is vice chairman of the Republican Governors Association and a possible contender for the 2016 GOP presidential nomination.

“There are still too many folks who would tell you the president’s unpopular, Obamacare is unpopular and when your opponent is self-destructing you stay out of his way — just make this election a referendum on that,” Jindal said in an interview.

“I think that’s a huge mistake,” he added. “If we want to earn the majority, we have to be offering detailed policy solutions, detailed ideas of what we would do differently. I don’t think it is enough to say, ‘Just repeal Obamacare.’ ”

Now, nearly 3.3 million people have enrolled in a health plan between Oct. 1 and Feb. 1.

Polls indicate that the Affordable Care Act continues to be unpopular, but the intensity of anger about it may be dissipating. Other issues — principally jobs and the economy — are greater concerns for most voters.

Moreover, while the GOP-led House has now cast 49 votes to repeal or strip funding from the health-care law, surveys show that a majority of Americans would rather see it proceed — albeit with course corrections. Although Republican candidates are virtually unanimous in their condemnations of the legislation, the party has not coalesced around any ideas for replacing it.

And a deeper dive into the numbers reveals another paradox. Although opposition narrowly outran support for the law in a Washington Post-ABC News poll in January, 49 percent to 46 percent, respondents by a much larger margin said they trusted Democrats more to handle health care, 44 percent to 35 percent.

The problems with the law have receded from the headlines, as the administration has fixed most of the Web site problems that plagued the rollout. Enrollment in the federal and state health insurance marketplaces now exceeds 4 million.

Still, nearly every day seems to bring a new round of skirmishing between the parties over the law.

The Republicans’ “fixation on repealing the ACA comes at their own peril, as the political landscape around the Affordable Care Act has shifted in Democrats’ favor,” Kelly Ward, executive director of the Democratic Congressional Campaign Committee, wrote in a memo that the House Democrats’ campaign organization blasted to its e-mail list Wednesday. “Democrats are now on offense over the Affordable Care Act, gaining the political high ground as benefits kick in and provide the ammunition to put Republicans on their heels over the costs of repeal.”

To which Republican National Committee spokeswoman Kirsten Kukowski retorted in another mass e-mail: “Congressional Democrats proudly gave us Obamacare. Given the rash of negative stories about how the law is adversely affecting millions of Americans — through higher costs and canceled policies — we think it’s only appropriate for Democrats to spend the next year apologizing for ramming Obamacare through Washington.”

The GOP’s message may well evolve between now and November, but the most tangible early indicator — advertising spending by conservative groups against Democratic candidates — shows how intensely it is focusing on the health-care law.

“It has been the predominant focus of both our grass roots and our advertising efforts,” said Tim Phillips, president of Americans for Prosperity, the primary political operation of a donor network backed by billionaire industrialist brothers Charles and David Koch.

Of the roughly $30 million the group has spent on ads since August, Phillips said, at least 95 percent has gone toward spots about the health-care law.

Democrats have been tracking that spending to help gauge what their candidates will be facing.

In Senate races, where control of the chamber is on the line, all but $240,000 of the $21.2 million that super PACs are spending on television advertising has gone into attacks centered on the health-care law, said Matt Canter, deputy executive director of the Democratic Senatorial Campaign Committee. The exceptions were ad buys in three states that criticized Democratic senators for supporting President Obama’s judicial nominees.

Phillips insisted that Americans for Prosperity’s money has been well spent.

“It’s resonating now,” he said of the negative advertising. “If you look at the job-approval rating of these members we’re holding accountable, their job approvals are going down. Really, there’s been no other exchange of ideas and issues in their states. There is no other issue than Obamacare.”

Republicans also say that by focusing on the law, they are sending a broader message — “a much bigger issue, and that issue is credibility and competence,” said Brad Dayspring, communications director for the National Republican Senatorial Committee.

Some Democrats agree that some of the attacks have been effective.

“It seems to be working,” said Gov. Mike Beebe of Arkansas, where Sen. Mark Pryor, a fellow Democrat, is engaged in a difficult reelection battle.

“That’s the only thing they are running against him on,” Beebe said of how the health-care issue is playing in Pryor’s race. “And right now, it’s a dead heat, if you believe the polls. Frankly, I don’t know what else they’ve got to run on. And frankly, in our state, as across the South, there is a huge dislike for what they refer to as Obamacare.”

But while animus toward the Affordable Care Act remains, most Americans appear to be more worried about other things.

In August, when Gallup asked Americans to name the country’s top problem, 25 percent said health care — putting it higher than any other issue.

In a survey released Feb. 17, only 15 percent said health care was the biggest problem. It ranked fourth-highest — after unemployment and jobs; the economy in general, and dissatisfaction with government and politicians.

“While health care is a very important issue, Republicans must focus on what is the overwhelmingly top issue — jobs and the economy, just like they did in 2010 with the question, ‘Where are the jobs?’ ” said David Winston, a pollster who advises House Speaker John A. Boehner (R-Ohio).

In Winston’s view, it is a myth that the last midterm election was swung by voter outrage about Obama’s health-care proposal, which was then being debated in Congress.

Only 18 percent in the 2010 exit poll ranked health care as the nation’s top issue, compared with 63 percent who felt that way about the economy. And those who did put health care at the top were slightly more likely to have voted Democratic than Republican.

The vehemence of the GOP base against the Affordable Care Act is so intense that it can be perilous for Republican candidates to suggest that there is any part of it that is salvageable.

Some organizations are offering a mixed message, which is more evidence that the politics of health care are far from clear-cut.

The U.S. Chamber of Commerce is running ads in Florida attacking Democratic House candidate Alex Sink for supporting legislation that it calls “a disaster for families and seniors.”

But in a “State of American Business” address last month, chamber President Thomas J. Donohue said that despite his organization’s efforts to block the passage of the measure, “The administration is obviously committed to keeping the law in place, so the Chamber is not out opposing it. We’ve been working pragmatically to fix those parts of Obamacare that can be fixed,while doing everything possible to make regulations and mandates as manageable as possible for businesses.”

Scott Clement, Peyton M. Craighill, Alice Crites and Tom Hamburger contributed to this report.