Axelrod dismissed the lawsuits, saying the Obama administration is very confident the health care bill "will withstand those legal challenges.
"First of all, every single major piece of legislation that's ever been passed in this country has engendered lawsuits. That's the nature of our system, and we expected that," Axelrod said on "GMA." "We're not concerned about these lawsuits."
House Minority Leader John Boehner today assailed the lack of bipartisanship on the bill.
"By signing this bill, President Obama is abandoning our founding principle that government governs best when it governs closest to the people," said Boehner, R-Ohio. "Never before has such a monumental change to our government been carried out without the support of both parties. This debate has fostered unprecedented division at a time when this nation needs to come together and address the serious challenges we face."
Under the health care bill, by 2014 most Americans would be required to have health insurance or pay a fine, with the exception of low-income Americans. Employers would also be required to provide coverage to their workers, or pay a fine of $2,000 per worker. Companies with fewer than 50 employees, however, are exempt from this rule.
ABC News' Z. Byron Wolf and Jonathan Karl contributed to this report.