Conservative group Heritage Action isn't happy that Senate Majority Leader Mitch McConnell suggested working with Democrats if Republican efforts to partially repeal and replace Obamacare fails.

McConnell, R-Ky., said on Thursday that if Republicans can't reach agreement on a bill to partially repeal the law, it would work with Democrats to stabilize the law's exchanges. Heritage Action CEO Mike Needham said the comments will make passing a conservative healthcare bill harder.

"Talk of a bipartisan bailout of Obamacare would have two major effects: It would embolden Republican moderates as they continue to hold out in attempt to keep as much of Obamacare on the books as possible, and it would undermine honest efforts that empower states to get out from under Obamacare's burdensome regulations," Needham said.

He added that if Republicans work to bail out the law's exchanges on the individual market, which is used by people who don't have insurance through work, "the results will be catastrophic for the party."

Needham pointed out that Republicans have pledged for seven years to repeal Obamacare.

The comments come a few days before the Senate is expected to reconvene after a week off. Republicans remain divided on key parts of a healthcare bill it announced several weeks ago, with conservatives complaining it doesn't do enough to repeal Obamacare and centrists concerned about major cuts to Medicaid and tax credits.