WASHINGTON — When the Republican National Committee gathers for its winter meeting here on Wednesday, the action will start a few hours late to accommodate anyone who wants to stop first at the March for Life, the annual anti-abortion demonstration on the National Mall. And if they need a lift to the meeting afterward, they can hop on a free shuttle, courtesy of the Republican Party.

“We thought it only fitting for our members to attend the march,” said Reince Priebus, the party chairman.

Abortion is becoming an unexpectedly animating issue in the 2014 midterm elections. Republicans, through state ballot initiatives and legislation in Congress, are using it to stoke enthusiasm among core supporters. Democrats, mindful of how potent the subject has been in recent campaigns like last year’s governor’s race in Virginia, are looking to rally female voters by portraying their conservative opponents as callous on women’s issues.

“Republicans have turned the floor of the House into the battleground for their relentless war on women’s health care and freedoms,” said Representative Steve Israel of New York, the chairman of the Democratic Congressional Campaign Committee. “Every time they launch another extreme attack against women’s rights, they lose more ground with women voters.”