WASHINGTON >> When the Republican National Committee gathers for its winter meeting here 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 Rep. Steve Israel of New York, 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.”

Aware that their candidates at times have struck the wrong tone on issues of women’s health, Republicans in some states are now framing abortion in an economic context, arguing, for example, that the new federal health law uses public money to subsidize abortion coverage. In the House in the coming weeks, Republicans will make passing the No Taxpayer Funding for Abortion Act one of their top priorities this year.

Democrats say their success this year will depend on how close they can come, given lower turnout, to President Barack Obama’s overwhelming margins with female voters; in 2008, he enjoyed a 14-point advantage among women, and in 2012, it was 12 points.

The fraught politics of women’s health care are already surfacing, as restrictions on abortion are appearing on state ballots and becoming the focus of debate in congressional races — many in places like North Carolina and Colorado that could hold the key to whether Republicans can sweep Democrats from power in the Senate and maintain their grip on the House.

“I don’t think this is a niche issue anymore,” said Drew Lieberman, a vice president at Greenberg Quinlan Rosner Research, a political consultancy concern, who has advised Democratic congressional candidates and has done polling for NARAL Pro-Choice America.

In North Carolina, Sen. Kay Hagan, a Democrat in a difficult re-election fight, and her allies plan to make an issue of the new restrictions on abortion approved by the Republican-led state Legislature.

In Colorado, where Sen. Mark Udall, a Democrat, says anger over the Affordable Care Act could hurt his chances, social conservatives have succeeded in placing a constitutional amendment on the ballot that would enshrine legal protections for fetuses. Even if it fails, similar “personhood” measures in Colorado and elsewhere have given Republican turnout a boost in years past.

In Oregon, Sen. Jeff Merkley could face a similar situation if supporters of an initiative there succeed in getting an anti-abortion measure with a fiscally conservative twist on the ballot: The measure seeks to outlaw the use of state funds to pay for any abortion unless the mother is in grave medical danger.

“We don’t make this a pro-life thing,” said Jeff Jimerson, who is organizing the petition drive. “This is a pro-taxpayer thing. There are a lot of libertarians in Oregon, people who don’t really care what you do, just don’t make me pay for it.”

Coupling the issue of abortion with a subject important to Republicans’ Tea Party followers — government spending — is one way the party is recalibrating its election-year message. Republicans say that by framing the abortion debate in terms of fiscal conservatism, they can make a connection to the issue they believe will ultimately decide who controls Congress next year — the Affordable Care Act.

“For a lot of members politically it ties into the issue they want to be talking about this election, which is Obamacare,” said Tom McClusky, vice president of government affairs for the March for Life.

Republican presidential candidates have almost universally opposed abortion rights. When Arlen Specter, then a Republican senator from Pennsylvania, ran for president in 1995 and declared he wanted to “take abortion out of politics,” the right balked, and his candidacy was short-lived. But Republicans do see a danger in talking about it the wrong way.

“It’s a matter of tone as well as substance,” said Ralph Reed, chairman of the Faith and Freedom Coalition, who noted how Republicans hurt themselves in 2012 by picking congressional candidates like Rep. Todd Akin of Missouri, whose infamous “legitimate rape” comments cost him his Senate candidacy and put his entire party on the defensive over women’s issues.

“What do they want us to talk about?” Reed said. “Rape and incest. What should the pro-life candidate talk about? Late-term abortions, sex-selection and Kermit Gosnell.” Gosnell was convicted in Philadelphia last year of murdering babies after failed abortions.

Priebus, the Republican chairman, will attend the March for Life this week, rare for a party leader. So will Eric Cantor, the House majority leader. In years past, Republican presidents have addressed the march by phone or video message to avoid speaking in person.

Nowhere was the power of the abortion issue more evident recently than in the governor’s race in Virginia, where the Democratic candidate, Terry McAuliffe, won in November in part because women preferred him by 9 percentage points over the Republican, Ken Cuccinelli, whom Democrats portrayed as extreme on women’s issues.

Nearly one-third — about $4.6 million — of the $16.4 million that Democrats and their allies spent on broadcast television advertising in Virginia last year dealt with abortion or birth control, according to an analysis by Kantar Media’s Campaign Media Analysis Group, which tracks political advertising.

Abortion rights groups have built targeting models that allow them to predict an individual voter’s position on women’s health issues. These models, along with similar ones built by the Obama campaign, were factors not just in Virginia last year but also in Democratic electoral victories in 2012.

One state that NARAL and Planned Parenthood are studying is North Carolina, where they see parallels to Virginia. Demographic changes there are giving Democrats hope that it could swing back into their column.

One of the leading contenders to be Hagan’s opponent in November is Thom Tillis, speaker of the state House, who voted for the tough restrictions on abortion. Democrats believe that would set them up to make the same kinds of sharp attacks that helped them prevail over Cuccinelli in November and over Mitt Romney in 2012.

While Democrats say such measures seeking to restrict abortions could stir votes, they acknowledge the limits of midterm turnout. “Off-year elections are difficult,” said Cecile Richards, president of the Planned Parenthood Federation of America. “You have lower turnout, and a lot of drop-off voters are women. So in a lot of ways, making sure women are aware and voting is important.”