DENVER – Republicans have won points with many voters by promising a conservative overhaul of taxes and spending, but Democrats are working hard in the closing weeks of the campaign to convince voters that a conservative social agenda is waiting in the wings, too, should Republicans be elected in large numbers.

Abortion rights is the flash point, being wielded by the left in hard-fought races from New York’s contest for governor, to Senate races in Florida and California, as Democratic candidates or groups try to rally their base and attract moderate Republican or independent women – a slice of the electorate that is even more coveted than in years past.

It used to be Democrats who feared "wedge" issues; they allowed Republicans to cleave off conservative Democratic voters. But this time around, Republicans want to talk about economic anxiety – widely shared by voters, polls say – rather than narrow social issues that might frighten off moderates.

The Democratic strategy is at least drawing the attention of voters. But it comes with a risk, too: Does selling the idea that Republican fiscal warriors are social zealots in disguise send a shiver of fear down voters’ spines, or make Democrats look like they are avoiding the subject on most voters’ minds?

One contentious commercial in New York shows women in a police lineup who, the voice-over says, would be turned into criminals if Carl P. Paladino, the Republican candidate for governor and abortion opponent, beats Andrew M. Cuomo, the Democrat.

In the bruising race for a Senate seat here in Colorado, one ad features a Denver obstetrician in her scrubs, saying women will lose control of their bodies if Ken Buck, the Republican nominee, wins. Another, from the Democratic Senatorial Campaign Committee, says privacy is at stake with a Buck victory over Sen. Michael Bennet, a Democrat.

The Buck campaign has said the attacks are simply an attempt to change the subject.

"The No. 1 issues are jobs and the economy, and Michael Bennet can’t run on that," said Owen Loftus, a spokesman for the Buck campaign. "It’s a desperate effort by a desperate campaign."

Loftus said Buck believed that life begins at conception and opposed abortion even in cases of rape and incest, as the ads say, but that his focus as a senator would be the economy.

Few Democrats think abortion alone will turn this year’s midterm elections for them; polls show Republicans leading in a generic "Which party would you vote for the Congress?" question. Here in Colorado, Democrats say the abortion issue more broadly conveys the message to moderate voters that Buck does not speak for them.

"People are growing more and more concerned about Ken Buck’s policies on the whole," said Trevor Kincaid, a spokesman for the Bennet campaign. "Those polices are out of touch with mainstream Colorado."

Bennet, a former city official in Denver, was appointed last year to fill a Senate seat vacated by Ken Salazar, a Democrat who is now secretary of the interior. In trying to tie social concerns to economics, Bennet on Tuesday unveiled a new agenda to advance opportunities for women, as business owners, workers and mothers. Protecting their rights to safe, legal abortion, he said, was part of that same fight.

But whether Buck is out of touch, or exactly in touch with his supporters, he has staked out some very conservative positions. He has suggested, for example, that Social Security and health care could perhaps be better handled by the private sector. (Though he later said he opposed privatizing Social Security.)

He also endorsed a ballot measure, Amendment 62, which would confer legal rights to "every human being from the beginning of biological development." That endorsement opened him up to charges that he wants to make some common forms of contraception illegal, including birth control pills, which can hinder the attachment of embryos to the uterine wall.

Buck, a county district attorney north of Denver who is backed by the Tea Party, recently withdrew his endorsement of the "personhood" amendment, and now takes no position. His spokesman, Loftus, said at least three times in a telephone interview that Buck did not want to ban birth control pills.

But the new fight over abortion and the voting clout of women also says a lot about Colorado itself – and its contradictions.

It was among the first states in the nation, in 1967, to loosen restrictions on abortion. Then, in 1984, it became the first state to ban the use of state money for abortions in a referendum.

Women have achieved some power in politics here, but never the top jobs. Colorado currently has the highest percentage of women in its legislature in the nation – 38 percent – but has never had a woman serve as governor or U.S. senator.

New York Times/CBS News national polls also say that the political divide between men and women – more men than women gravitating toward Republican candidates, a pattern dating back to Ronald Reagan’s election as president in 1980 – is bigger than average heading into November. And between Bennet and Buck, that gender gap is immense. A CNN poll released in late September said that men were 15 percentage points more likely than women to support Buck, while women were 16 percentage points more likely than men to prefer Bennet.

"This isn’t a gap, it’s a canyon," said Susan Carroll, a senior scholar at the Center for American Women and Politics at Rutgers University, who said the average gender difference in presidential races was about 7 or 8 percentage points.

But whether the new ad barrage is about women, or abortion, or something else entirely, it has caught the attention of Stacy Gholz, a student who was walking through downtown Denver on a recent morning.

Gholz, 23, is the kind of voter who could decide the race. She described herself as unaffiliated and undecided, a Catholic, but a believer in abortion rights, brought up as a Republican but married to a Democrat. She voted for George W. Bush in 2004 and Barack Obama in 2008.

"I don’t think he has the right to tell a female what she can and cannot do with her body," she said, referring to Buck. "But I’m still working it out," she added, regarding her vote.