WASHINGTON — The top Republican in the Senate, Mitch McConnell of Kentucky, has a reputation as a shrewd tactician and a wily strategist — far more than his younger counterpart in the House, Speaker Paul D. Ryan.

So the Senate majority leader’s decision to create a 13-man working group on health care, including staunch conservatives and ardent foes of the Affordable Care Act — but no women — has been widely seen on Capitol Hill as a move to placate the right as Congress decides the fate of President Barack Obama’s signature domestic achievement.

But Mr. McConnell, with only two votes to spare, could find that the Senate’s more moderate voices will not be as easily assuaged as the House’s when a repeal bill finally reaches a vote. Republican senators like Susan Collins of Maine, Lisa Murkowski of Alaska and Bill Cassidy of Louisiana may prove less amenable to appeals for party unity and legislative success when the lives and health of their constituents are on the line.

And certain issues, like efforts to reverse the expansion of Medicaid under the Affordable Care Act, are sure to receive more attention in the Senate than they got in the House. The prospect of higher premiums for older Americans living in rural areas will also loom larger in a chamber where Republicans from sparsely populated states hold outsize power.