Liberals and conservatives agree on one thing: They both hope that the battle over birth control that has erupted in Washington has far-reaching repercussions in this year’s elections. A new polling memo, published Thursday by the Democratic firm Democracy Corps, sheds new light on how much it could matter.

The Democracy Corps poll finds that one of the most important factors powering President Obama’s gains against likely Republican nominee Mitt Romney has been the president’s improving numbers among unmarried women, a key pillar of the present and future Democratic coalition.

Among this group, Obama now leads Romney 65 percent to 30 percent, and there has been a net 18-point swing toward the president since November.

After unmarried women dropped off for Democrats in 2010 and were slow to return to the party in 2011, Obama is now approaching the level he won in 2008, 70 percent.

Unmarried women will be important to Obama’s success at rebuilding his 2008 coalition in time for reelection, something that already seems to be under way, as the Atlantic’s Ronald Brownstein has demonstrated. This constituency is complex and diverse; it includes young women who have never married, divorced women and widows, and it cuts across class, racial, income and geographic lines.

Various factors — the improving economy; the drawn-out Republican nomination process; the GOP’s sinking approval ratings — already seem to be driving this group’s move back toward Obama. And the pitched battle over birth control could continue to galvanize and unite this group behind him, particularly if Romney is forced to embrace the conservative position. The Democracy Corps poll also tested the two sides’ position on this issue and found that 61 percent of unmarried women side with the Democratic one.

If Democrats play this right, they could encourage the perception that the Republican Party is lost in a social-issues wilderness, perhaps hastening the already-widening gender gap that will be so crucial to the outcome this fall.

Greg Sargent wrote this for The Washington Post.