Story highlights Obamacare enrollment deadline has passed

But Republicans have embraced it as a campaign issue

What about the question of "Obama fatigue" for voters?

David Jolly's win in Florida partly attributed to anti-Obamacare sentiment

Republicans are going all in, hoping that the payout is big. Like control of the Senate, big.

Their big bet: Obamacare.

The deadline to enroll in the Affordable Care Act for the year has come and gone. The Obama administration is touting the enrollment numbers as a successful first year, but Republicans think voter anger over the law is here to stay. And so, Republicans running for House and Senate continue to make it central to their campaign.

In the Arkansas Senate race, Republican challenger Tom Cotton is using Obamacare to fund-raise for his race against Democratic incumbent Mark Pryor. The first screen on Cotton's website is a plea for contributions that says, "Obamacare is so bad that Obama doesn't want it. Tell him neither do I."

Fund-raising schemes and campaign advertisements are central to Republican races in red and swing states around the country.

Republican confidence

When Republican David Jolly beat Democrat Alex Sink in Florida's special election for the 13th Congressional District in March, Republicans attributed the win in part to the health care law.

"His (Jolly's) victory shows that voters are looking for representatives who will fight to end the disaster of Obamacare," Republican National Committee Chairman Reince Priebus and co-chair Sharon Day said in an email blast to reporters after the results were tallied.

The deep-pocketed group Americans for Prosperity is playing in dozens of races around the country, and its sole weapon is Obamacare.

"We do want to make sure that Obamacare is the number one issue in the country," Tim Phillips, president of AFP, said in a recent interview.

The organization, backed by the wealthy partisans David and Charles Koch, has already spent more than $30 million this election cycle and plans to spend a great deal more to ensure that Democrats "have to explain" their support of the law.

Public opinion

Republicans believe they have a winning issue, insisting that Americans are opposed to the law. And most polling is on their side.

According to the most recent survey conducted just over a week ago by CBS News, 53% of Americans gave the law a thumbs down, compared to 41% saying they approve of it. That's in line with most polls.

But that could be starting to change. A Kaiser Family Foundation poll released last week found that the gap between approval and disapproval of the law narrowed to 8 points. And a new Washington Post/ABC poll out Monday found that 49% support the law compared to 48% who don't.

Public action

While polls are indicative of voter opinion, they don't indicate voter action. What does, however, is enthusiasm, and Republicans have that on their side. In a midterm election, when people are less likely to vote, voter turnout is critical and Obamacare gives Republicans an advantage.

"This data pretty clearly shows that even though attitudes regarding the ACA are 'baked in' with voters (68% feel strongly one way or another about the issue), the intensity is clearly on the negative side, as GOP voters clearly dislike the new law more than Democrats are in love with it," said GOP pollster Neil Newhouse , a co-founder of Public Opinion Strategies.

Voter apathy is a challenge that Democrats must overcome.

Republican strategy: Invoke doubt

Republicans are hitting a nerve when it comes to Obamacare. They are appealing to their base's mistrust in the President.

Republican Sen. John Barrasso on "Fox News Sunday" alleged the administration is "cooking the books" regarding the program's rollout numbers. This includes the latest number that more than 6 million have enrolled.

And Republicans constantly raise questions: Who are the people enrolling and did they have health insurance beforehand?

Obamacare was pushed by the President and passed by Congress in 2010 with no Republican support as a way to narrow the gap between those with coverage and the tens of millions without it.

White House spokesperson Jay Carney said Republicans are grasping at straws as the law takes hold and people begin to see benefits.

"I know it leaves them with the need to go back to the drawing board when it comes to other means of trying to attack a law that is providing opportunity and security to millions of Americans," Carney said.

Republican risks

Pounding an issue into the ground does bring some risks -- voter annoyance.

A Kaiser Family Foundation poll found that 53% of Americans are tired of hearing about the law.

Republican pollster Whit Ayers said there's a more powerful factor in voter fatigue: Obama himself.

Six years into a President's term, "people get tired of that person's leadership," he said. "Especially this President's."

Democrats' challenge

The goal is to get Democrats to the polls.

Democrats, however, have a more complicated role that consists largely of defense. While they are being attacked on the campaign trail over the law, they have decided to respond in a multipart way by saying that some of the law is great, but some parts need to be fixed.

That's exactly what endangered Democrats, including Sens. Mary Landrieu of Louisiana and Alaska's Mark Begich, did when they and several colleagues penned an op-ed laying out the parts of the law that they said need to be changed.

Rep. Steve Israel, chairman of the Democratic Congressional Campaign Committee, an organization that works to elect Democrats to Congress, is fighting back by highlighting the "cost of repeal."

The organization is telling stories of people who live in districts with contested congressional races who say they could not afford health coverage without the Affordable Care Act.

"Americans do not want to repeal the ACA and go back to the days when insurance companies had free rein over health care; they want it fixed and improved. But this Republican Congress is obsessed with a repeal that will force hardworking families into bankruptcy and let insurance companies deny care and drop coverage," Israel said.

It's a difficult way to convince people to turn out to vote, even if public opinion drastically changes in favor of the law.

In the March Florida special election in a swing district in a swing state, the only test case analysts have to monitor in the current political climate, Sink embraced only parts of the law. She also talked about what needs to be fixed, a strategy that didn't work.

But as of now, Democrats don't want to be talking about it. That's why they are focusing on economic issues such as minimum wage and equal pay for women.

New York Sen. Chuck Schumer, who is a member of Senate Democratic leadership, said people aren't focused on Obamacare.

"Most Americans want to hear something positive. 'What are you going to do for me?' Republicans are going to give them no answers on that," Schumer said

But former President Bill Clinton said Democrats cautioned against running from the law they championed and passed.