The battle over Obamacare may rage on for years, and it will certainly play a major role in next year’s House races. Republicans say that since the law is unpopular, their repeal message must be a winner for them. Dems allow the law is unpopular but argue that people want reform more than repeal — and favor individual ACA reforms — so their message that Republicans would only return us to a pre-reform insurance-industry-unbound free for all will ultimately carry the day.

But in the end, the side that wins the war over Obamacare may be the one that most convincingly positions itself as the party that wants to fix our health care system.

Liberal groups — the White House-allied Americans United for Change, the Center for American Progress, and SEIU — just held a conference call to roll out the results of a new poll of 2014 likely voters by Dem pollster Geoff Garin on Obamacare. The poll seems designed partly to put some spine into 2014 Dem candidates who might be tempted to run from engaging the battle against Republican candidates pushing repeal. The poll’s key finding is that whatever Obamacare’s unpopularity, full repeal is a losing message:

Only 36 percent of all voters say they would prefer Obamacare to be repealed, whereas a 40 percent plurality would prefer to leave the law as it is (15%) or just make minor changes (25 percent). Another 18 percent of voters support making major changes in the ACA. Among the key grou who are undecided in the 2014 generic Congressional ballot, only 39 percent want to repeal Obamacare.

“The clear message here to Republicans is that they are out of kilter with the electorate because of their obsession with repealing Obamacare,” Garin said on the call. “This sends a very strong message to Democrats that taking the initiative, being proactive in making the case against repeal, and making the case for fixing and improving the law, is a very strong political position for 2014.” This roughly mirrors what the more nuanced public polling has shown.

What does this mean for 2014? I checked in with David Wasserman, the nonpartisan analyst who tracks House districts and races for Cook Political Report. He argued persuasively that as Obamacare kicks in, both sides face political perils.

Cook Political estimates that there are roughly 35 House seats in play, 23 held by Dems and 12 by Republicans — all seats with plenty of independent voters. “Whichever candidates can emerge closer to the middle on health care will have a better shot of winning over that critical mass in the middle,” Wasserman says.

As Wasserman sees it, Dems face the real danger that Obamacare implementation problems (and press coverage of those problems) could further turn off voters in the middle. “They have a very important strategic decision to make — whether to advocate just for keeping the law or advocate for fixing the law, which could let voters know they are aware of its flaws,” Wasserman says.

But, Wasserman notes, Republicans risk being so tied to a repeal message (thanks in part to primaries) that they risk looking as if they have no interest in fixing the health care system at all — which could alienate key swing constituencies in House races. “They don’t prefer an all-or-nothing approach,” he says. “They want to see compromise.”

“Democrats are preaching keep; Republicans are preaching repeal,” Wasserman says. “The winning candidates in 2014 will most likely be preaching fix.

If this is right, there’s reason to believe it could marginally favor Democrats, particularly if Republicans remain wedded to an all out battle to destroy Obamacare completely while offering nothing meaningful to replace it. Dems have the option of standing behind Obamcare’s general goals — expanding coverage to the uninsured, reining in insurance industry abuse, etc. — while allowing for problems with implementation and advocating for a constructive, make-changes-as-you-go approach. They can do that while calling out Republicans for refusing to offer any solutions of their own. This does not have to mean running from the law wholesale, and it shouldn’t be too hard a case to make.

Greg Sargent writes The Plum Line blog, a reported opinion blog with a liberal slant -- what you might call “opinionated reporting” from the left.