"They won't be able to charge you more because you're a woman."

With that pronouncement (among others) after the Supreme Court ruled Thursday to uphold the Affordable Care Act, President Obama hailed the 5-4 decision.  But he was also staking a claim to a key swing demographic in the upcoming presidential election for whom "Obamacare" could be a top issue. 

Obama was referring to insurance industry standards in which women were charged more than men on the grounds that they require more health care. A report  from the National Women's Law Center earlier this year indicated that most insurers charge women more except in states where gender bias is prohibited. And individual policies often exclude maternity coverage for women, the center said.

But in two years, that gender differentiation will be prohibited nationally, unless Republicans succeed in their efforts to overturn the law before it fully takes effect in 2014. 

While Obama touted the costs savings for women, other groups cheered — or jeered -- the Supreme Court's decision. 

Planned Parenthood lauded the fact that women will get insurance coverage for birth control with no co-pays starting in August. The organization said that coverage could save women up to $600 a year.

The National Partnership for Women & Families noted the law’s extended coverage of adult children on their parents’ plans and a prohibition on refusing coverage because of preexisting conditions.  

And, in 2014, women - and men - who are uninsured are expected to be able to find affordable coverage. 

But not all women are happy with Thursday's decision. 

"Obama lied to the American people. Again. He said it wasn't a tax. Obama lies; freedom dies," tweeted former Alaska governor and 2008 vice presidential candidate Sarah Palin shortly after the decision. (Earlier thus week, Palin repeated her "death panel" claims about the law, earning four Pinnochios from The Washington Post's Fact Checker.)

Jessica Peck, a Denver lawyer and conservative political activist, said the upholding of the health care law shocks and frightens her. 

"On the surface, this is a pro-woman decision. If you peel back the layers, however, it promises to be incredibly destructive," she wrote in an e-mail. "The government has authorized itself to tell us what we can do with our bodies in a way never witnessed in this country before... Government's ability to monitor our compliance with insurance mandate will inevitably mean that it is monitoring our health decisions."

Peck, a single parent, said earlier this year that she was uninsured for several months - and that she should have the option to be uninsured. 

Suburban women in Colorado and other swing states are expected to be essential to Obama's strategy in his race against GOP candidate Mitt Romney. While Peck and other conservative women may use the decision as part of their rationale to reject the president in the fall, Obama has to hope that portions of the law that have already taken effect will sway unaffiliated women to vote for him.  

Sandra Fish teaches journalism at the University of Colorado and has reported on politics in Iowa, Florida and Colorado. Follow her on Twitter at @fishnette