"I think there's just a fatigue amongst elected Republicans on Obamacare," said Dan Holler, communications director for Heritage Action, in an interview conducted last month. "There seems to be this hesitancy to talk about Obamacare much."

In part, any fire dies down over five years. But the temperature on the right also got a lot lower after 8 million people signed up for coverage through the healthcare law's exchanges.

Heritage Action and some of its closest allies—Senators Mike Lee and Ted Cruz—tried to stoke the flames once Burwell's nomination passed (with bipartisan support) out of committee and came to the Senate floor. But they only went so far, demanding answers to a series of questions about the healthcare law.

"Until the President agrees to offer meaningful relief to the millions of people hurt by Obamacare, we should not confirm this nominee," Cruz said in a statement following Wednesday's procedural vote.

Even that, however, is significantly dialed back from Cruz's rhetoric ahead of last year's government shutdown, when he taunted his fellow Republicans by arguing that a vote to keep the government open was "a vote to fund Obamacare."

It wasn't—almost all of Obamacare's funding was separate from the bill Cruz blocked. But precisely because of the traits that make Burwell hard to oppose—her talent for management, and her appetite for policy—a vote for Burwell probably is a vote that will help the Obama administration more effectively implement the Affordable Care Act.

Yet Cruz hasn't tried seriously to put his party on the spot. When asked last month whether Republicans should force a broader confrontation over the Burwell nomination, Cruz responded with a well-worn line about using every opportunity to showcase Obamacare's failings.

None of this is to say that Republicans now support Obamacare, which they very much do not, or that it won't be a problem for Democrats in this year's midterms, which it will.

The law is unpopular, and its critics feel more strongly than its supporters. But with public opinion locked in place for months, "Obamacare" has become almost a party-ID question or a buzzword, rather than a dynamic issue.

The Obamacare war has been a constant in politics since 2009, with peaks and valleys of intensity. The peaks have almost always been tied to some external development—from the law's passage, to the Supreme Court decision upholding it, to delays in the employer mandate, to the blundering launch of Healthcare.gov, to a wave of cancellation notices.

If past is prologue, don't bet against more delays and policy flubs by the administration. But barring any major mistakes, Republicans don't have a lot of openings left to force the healthcare law back into the headlines.

The GOP will get some mileage out of 2015 premium increases as rates trickle out over the summer. But at least so far, the hikes are far smaller than what most critics predicted. No one likes a 15 percent premium increase, but that doesn't look so terrible compared with critics' predictions that premiums would skyrocket by as much as 300 percent. Some carriers are even cutting their prices for next year.