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The White House and some Republicans who want to keep up efforts to repeal the Affordable Care Act have seized on a proposal aimed at giving states significant flexibility, though Senate leaders are suggesting they won’t revisit the health-care issue in the near future. The proposal, which Sens. Lindsey Graham (R., S.C.) and Bill Cassidy (R., La.) unveiled when the GOP’s primary legislation to overhaul the 2010 health-care law was faltering, is designed to let states craft their own health systems to some degree. (Hackman, 8/1)

Senate Majority Leader Mitch McConnell (R-Ky.) is leaving the door open for Republicans to take a second run at repealing ObamaCare after a GOP proposal failed last week. "We're continuing to score some of the options on healthcare," McConnell told reporters during a weekly press conference on Tuesday. "There's still an opportunity to do that." (Carney, 8/1)

Sen. John Cornyn (R-Texas) is urging Democrats to offer ideas on fixing the healthcare system, saying "fragile majorities" in the Senate force both parties to work together. "Democrats need to be more constructive rather than just continuing to bury their head in the sand about the fundamental problems with the Affordable Care Act," Cornyn, the No. 2 Republican, said from the Senate floor on Tuesday. (Carney, 8/1)

Dean Heller can’t win on Obamacare. He’s inflamed the left and right throughout the debate on repealing the law. And now the Nevada Republican is handing critics more ammunition by signing onto a new overhaul of Obamacare that has piqued the interest of the White House but nonetheless has little momentum. (Kim, 8/2)

Sen. Dean Heller’s vote to support a bill to repeal the 2010 health care law — while rejecting others — may make an already tough re-election campaign even harder. The Nevada Republican was already facing pressure from voters on the left and the right, his own party’s leadership and the White House going into last week’s Senate health care votes. That’s not all going away just because the votes are over. (Bowman, 8/1)

Even though Republican efforts to repeal the Affordable Care Act have died for the moment, it still was the biggest topic on the minds of several hundred people at a town hall hosted Tuesday by U.S. Rep. Justin Amash. The Cascade Township Republican heard from constituent after constituent that his support for a repeal was an injustice and that he should represent their interests. (8/1)