Story highlights Sanders called the House bill "the most anti-working-class piece legislation passed by the House" in modern history

The Senate Republican leadership is pressing for a vote on their overhaul later this week

Columbus, Ohio (CNN) If not for the promise of President Donald Trump's signature, the current Republican effort to shred Obamacare would have ended like so many others over the past seven years -- defeated at the pass.

But this time around, with an approving executive itching to sign their work, Republican leadership is pressing toward a comprehensive overhaul, ignoring pleas from Democrats on Capitol Hill for more open debate, and furiously whipping support from wobbly GOP legislators whose defections could imperil their progress.

Trump, for once, seems to be an afterthought. In conversations with more than two dozen attendees at weekend events headlined by Sen. Bernie Sanders to protest the Republican bill -- first in Pittsburgh, Pennsylvania, on Saturday night and then Columbus, Ohio, early Sunday -- the President's name never came up unprompted.

On the sidewalk outside a small concert venue in its Arena District, Columbus resident Kelly O'Rourke, 55, said the political tab for any potential harm the law might do to a grandson born with health issues or her own costs would come due on Capitol Hill.

"I'm going to blame (Senate Majority Leader) Mitch McConnell and the guys who have been there for a million years," she told CNN, dismissing the President's role.

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