Minnesota Gov. Tim Pawlenty (R) is joining a lawsuit challenging the constitutionality of the new health law over the recommendation of the state's top law enforcement official.
Pawlenty is a potential 2012 GOP presidential candidate and the lawsuit is one of the most highly-visible ways in which Republicans are trying to dismantle the measure.
Swanson did say that she would leave it up to the governor's discretion whether or not to join the suit.
Several states have joined the lawsuit that was originally filed by 13 states last month in a Florida federal court. Its backers believe their challenge will reach the Supreme Court, but the Obama administration has said the case is "completely without merit."
Pawlenty has sought to take a hard stance against the healthcare law since the debate over it began.
He has tacked to the right of former Massachusetts Gov. Mitt Romney (R), a potential 2012 challenger, by saying the universal healthcare stance he signed in his state is similar to the national law signed by President Barack Obama.
Romney has said the bill is significantly different and has called for the bill to be repealed.