Margot Lee, a volunteer for Enroll America's Get Covered America campaign, organizes her materials before canvassing in Englewood, N.J., in July. Michael Nagle/Bloomberg via Getty Images

WASHINGTON — Republicans can tick off myriad reasons they want to defund the Affordable Care Act (ACA). They say it will cause some premiums to rise, it is another example of the government meddling in the free market and restricting individual choice and it will put an undue burden on small businesses.

But some conservative members of the GOP, including Texas Sen. Ted Cruz, who embarked on a 21-hour speech on the Senate floor earlier this week to lay out his case against the law, have hinted at another reason they see the current fight over the budget and the debt ceiling as their last, best chance to stop the ACA. There is the possibility, they say, that the public might come to like the new benefits once the law is fully in effect.

"While the ultimate goal is to repeal the law in its entirety, defunding is a crucial step so we can stop the law from being implemented before Americans get hooked on the subsidies," Cruz told the online conservative publication The Daily Caller.

Sen. Roger Wicker, R-Miss., similarly indicated that it would be hard to repeal the law after the public had a chance to get accustomed to it.

"Anytime you get somebody used to a government program, there is a tendency to — for that program not to go away," he told NPR.

Wicker also said, "In the next two years, really, less than 10 percent of the American people will be on this type of subsidy. So I think there are going to be so many drawbacks that I don't see Obamacare getting exceedingly popular."

Polling consistently shows that even three years after its passage, the ACA remains divisive among the public. A New York Times poll released Thursday shows that 51 percent of Americans disapprove of the law. About 39 percent believe the ACA should be defunded or stopped in some other way.

But there is a chance that public opinion might follow the polling trajectory of other federal social programs, which were deeply unpopular before implementation and ultimately became widely liked.

Before Medicare was created in 1965, a Gallup poll from July 1962 showed that just 28 percent of Americans held generally favorable views of President John F. Kennedy's proposal, compared with 33 percent who didn't know what to make of it and 28 percent who disapproved.

"Obamacare is a home run by contrast," said Michelle Diggles, a senior political analyst with Third Way, a center-left think tank.

Today Medicare is broadly popular, although some GOP lawmakers have led efforts to cut benefits.

A more recent example comes from Medicare Part D, a provision — championed by Republican President George W. Bush in 2003 — that added prescription-drug benefits to the program. In April 2005, just as the measure began implementation, only 21 percent of the public had a favorable opinion, according to polling by the Kaiser Family Foundation and the Harvard School of Public Health.

Democrats, for their part, said the program was designed to benefit private insurers and pharmaceutical companies. Today about 90 percent of seniors are satisfied with their prescription-drug coverage under Medicare, and in 2010, Democratic lawmakers, even those who were originally opposed, voted to improve Part D as part of the ACA by closing a coverage gap long lamented by seniors.

Some analysts predict that the health care law as a whole will go the same way.

"It really wasn't until people started to gain access to these new benefits and actually get this new coverage and needed medicines that people started seeing those tangible financial and health-related benefits. That is really what started to turn public opinion," said Sabrina Corlette, a professor at the Health Policy Institute at Georgetown University. "And I think the same will be true for the health coverage under the ACA."