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Mr. Rahall is the only Democrat in the state’s three-member delegation to the House of Representatives. His loss would create West Virginia’s first all-Republican delegation in more than 90 years.

Mr. Obama’s health care law also is unpopular in West Virginia.

The national Republican Party, conservative super PACs and Mr. Rahall’s likely Republican opponent, state Sen. Evan H. Jenkins, have criticized Mr. Rahall for voting for the Affordable Care Act and for backing Mr. Obama’s plan to tax carbon emissions through a “cap-and-trade” system.

Mr. Rahall has insisted that he never voted for cap-and-trade, though he did vote for Mr. Obama’s 2009 budget that set the stage for it.

He will face a challenge in the state’s Democratic primary Tuesday from Richard Ojeda II, a retired Army officer. Mr. Rahall is expected to win.

Mr. Jenkins, who switched from the Democratic Party last year before his run for Congress, is unopposed on the Republican primary ballot.