Hillary Clinton speaks during a 'Women for Cuomo' campaign event on October 23, 2014 at the Grand Hyatt Hotel in New York, NY.National Journal

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Amid concerns about the bill's political fallout, House Republicans on Wednesday abruptly pulled legislation that would ban most abortions after 20 weeks. They were more right than they know to be worried.

A renewed effort to curb abortion rights carried severe risk not just for the House GOP Caucus but the party's eventual presidential nominee. Because in a race against Hillary Clinton, the GOP starts at a stark disadvantage among a very specific group of voters it needs to start peeling away from Democrats if it intends to take the White House: white, college-educated women.

These are mostly suburban, moderate voters who skew socially moderate but are hardly fiscally progressive; in other words, they're broadly supportive of abortion rights but generally opposed to higher taxes.

They also haven't been especially supportive of the current president. In 2012, Obama drew less support from them — 46 percent — than any Democratic presidential nominee since Michael Dukakis in 1988, despite winning reelection relatively comfortably.

Early polling suggests they're poised to snap back into the Democratic column if Clinton is the Democrats' presidential nominee — as a poll last week from the liberal group Democracy Corps underscored. In hypothetical matchups with GOP presidential candidates, the survey found she leads among college-educated white women 56 percent to 39 percent. That's a 23-point swing from Obama's performance in his last campaign.

Other polls have found a similar gap: A July survey from Quinnipiac University (whose cross-tabs were provided to National Journal) that pitted Clinton against five potential GOP presidential nominees found her drawing no less than 53 percent among these white-collar voters.

What's remarkable is the spike in support among college-educated white women hasn't translated into a greater advantage with white women without a college degree. In the Democracy Corps poll, Clinton earned just 35 percent of their support in a matchup with a GOP nominee. That's lower than even Obama's 39 percent in 2012.

Quinnipiac over the summer found her earning slightly more support from them, but still failing to perform markedly better than the president.

Much can change in the next 18 months of campaigning, and Clinton's early advantage against Republican foes is a reflection in part of superior name recognition and a party already united behind her. But it's also clear that the strength of her candidacy will be rooted in her appeal to upscale white women, a bloc that often holds the decisive say in marquee presidential battlegrounds like the Philadelphia, Denver, and the Washington suburbs.

For the Republican Party, then, figuring out how to loosen her grip on them is paramount to winning the White House. Even if they can't match Mitt Romney's level of support, they can at least reduce her advantage enough that gains with other voter blocs — white-collar men, Hispanics, blue-collar women — provide a path to the presidency.

Which is why a Republican push on abortion is fraught. It's not that a single piece of legislation, voted on almost two years before the next Election Day, can alter the course of a presidential race. But the mindset it suggests — of a party eager to show off its new majorities at a federal and state level — could influence not just legislative action but the rhetoric and positions of its presidential candidates.

And putting abortion rights back on the minds of voters is hardly a good way to convince college-educated women to vote Republican, when the party's best arguments among this electorate rests in fiscal and foreign policy.

"What they're looking for, in particular, is the economy and jobs," said David Winston, a Republican pollster who has worked with House Republicans. "What they're looking for is, show me value in terms of what you're talking about to get this economy going."

Proponents of the legislation will point out, correctly, that most voters actually support a 20-week abortion-ban: A November poll from Quinnipiac found 60 percent of Americans back it. Whether voters would actually process the vote as a single issue or part of broader effort to curb abortion-rights, like GOP-led efforts to defund Planned Parenthood.

This article was updated at 9:53 p.m.

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This article is from the archive of our partner National Journal.

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