A new poll signals trouble for conservatives’ fight to repeal Obamacare: it’s losing steam in Republican-held House districts, which have been the national backbone of the cause.

The survey, released Monday by Democracy Corps, a Democratic firm run by former Bill Clinton aides James Carville and Stan Greenberg, asked voters in the most competitive House districts whether they prefer the Democrats’ push to “implement and fix” Obamacare or the GOP’s push to “repeal and replace” Obamacare.

In 50 Republican-held districts it found a 10-point swing in the direction of “implement and fix” from December 2013 to April 2014. Four months ago 47 percent chose “implement” while 46 percent chose “repeal.” This month it was 53 percent and 42 percent, respectively. (Charts via Democracy Corps.)

In “tier 1 Republican seats” — which the survey identified as the most competitive — the poll found an 10-point swing among voters in the direction of “implement” during the same time period.

Even among self-identified independents — who have long opposed Obamacare — the momentum is with implementation of the law: the poll found a 19-point swing toward the Democrats’ message. Fifty percent of them now want to keep and “fix” the law; 43 percent wanted to repeal and replace it.

The only region of the country where “repeal and replace” has gained traction over the last four months is the South — it picked up 6 points. Among white rural voters outside the South “implement and fix” gained a whopping 20 points; among rural voters generally it gained 11 points.

The poll, conducted from April 10-15, surveyed 2006 voters and has a margin of error of plus or minus 3.58 percentage points in the GOP districts. The charts above were included in the survey, which can be read in full below.