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That’s not the most important consideration for governors who face re-election in Republican states. Georgia’s Nathan Deal and Alabama’s Robert Bentley, who also face 2014 campaigns, initially set up advisory commissions to consider how to carry out the health care law, but they’ve since jumped ship. But, unlike others, Mr. Deal and Mr. Bentley aren’t eyeing national office.

Three Republicans viewed as potential national candidates — Rick Perry of Texas, Nikki Haley of South Carolina and Bobby Jindal of Louisiana — were full-throated opponents.