NEW YORK — A Republican-leaning independent group supporting Mitt Romney’s presidential bid is spending $11.1 million on new television ads aimed at women.

The ad campaign, set to begin Tuesday and run for a week in eight closely contested states, is part of a big push in the final three weeks before the Nov. 6 election.

Polls have shown President Barack Obama with a wide lead over Romney among women, but some surveys suggest that gap has narrowed recently.

The ad, “Sack It,” shows a woman watching one of Obama’s campaign commercials. “Mr. President, here’s what I want to know,” she says, asking about the jobs he has promised and wondering what the federal spending he has pushed for has produced.

She ends by saying, “My family can’t afford another four years like this.” The line echoes a theme Romney has repeated several times on the campaign trail in recent weeks — “We can’t afford four more years like the last for years.”

Steven Law, president of American Crossroads, the group behind the ad, said in statement that Obama’s “weak leadership has created a weak economy and a weaker America, and it’s time to turn this ship around.”

The group planned to air the new ad on national and local cable stations, and in Colorado, Florida, Iowa, Nevada, New Hampshire, North Carolina, Ohio and Virginia.

American Crossroads was co-founded by Karl Rove, the longtime political counselor to former President George W. Bush. The group and its affiliated nonprofit, Crossroads GPS, plan to spend $300 million to influence elections this year. The groups have spent $135 million on ads so far to back Romney.

The Crossroads groups are some of the biggest players in a constellation of independent organizations and political committees that are playing a large role in the presidential campaign. The groups can raise and spend unlimited sums to run ads on behalf of candidates as long as they do not directly coordinate with the candidates they support.

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