The health care law has been a tough sell around the country, but in several swing states where President Barack Obama and Mitt Romney will heavily contest, voters want the U.S. Supreme Court to strike down the president's signature domestic achievement.

A Quinnipiac poll released Thursday said voters in Florida, Ohio and Pennsylvania prefer to see the Affordable Care Act ruled unconstitutional.

In Florida, where Obama's decline among voters puts him in a statistical dead heat with Romney, a majority of voters want the health care law gone, 51-38; Ohio voters who also split their support between the two candidates feel the same way, 51-37 percent.

Meanwhile, there is much more support for the health care law in Pennsylvania, where the president enjoys an 8-percentage point lead over Romney. More voters say the justices should rule against the Obama administration, but by a much-narrower margin, 46-43 percent.

Voters in general have wanted to see either the entire law or just the insurance mandate provision tossed out by the high court. After the Supreme Court's historic March hearings on the law, a Washington Post-ABC News poll said in April a quarter of Americans wanted to see the law upheld; 38 percent wanted the entire law scraped and 29 percent want the mandate gone, with some of the law intact.