Appealing to a key constituency, President Obama said today that this year’s election could decide whether women get to keep newly won rights on health care and pay equity.

“The choice between going backward or moving forward has never been so clear,” Obama told a supportive crowd in Denver at the start of a two-day tour of Colorado.

Obama cited the benefits for women in the new health care law, such as free access to contraception and preventive care. He spoke of signing a bill setting new rules for pay equity lawsuits. And he cited the appointments of Supreme Court Justices Sonia Sotomayor and Elena Kagan.

Republican opponent Mitt Romney, Obama said, wants to “kill” the health care law and would likely appoint conservative judges willing to roll back women’s rights in a variety of areas.

“We’ve come too far to turn back now,” Obama said.

Most polls give Obama big margins over Romney among female voters; many of those same polls give Romney the edge among men.

Romney’s aides say Obama’s stewardship of the economy has been bad for all Americans, women as well as men.

“Hundreds of thousands of women have lost their jobs, poverty among women is highest in nearly two decades, and half of recent graduates can’t find a good job,” said Amanda Henneberg, a Romney spokeswoman.

In his Denver speech, Obama stressed the impact of the health care law, and how it is designed to attack gender disparities that have existed with health coverage and costs.

He was introduced at the rally by Sandra Fluke, the young woman described as a “slut” by talk-show host Rush Limbaugh after she testified before Congress about contraceptive policy.

Colorado is one of a dozen or so swing states that will decide the Nov. 6 election.

As Obama began his speech, with the crowd chanting “four more years,” the president said: “I tell you what — we win Colorado, I’ll get four more years.”

Obama ended his speech by saying: “If we win Colorado, we will win this election — we will finish what we started.”