March 23, 2010 -- President Obama signed the historic health care bill into law today, but Republicans are still fighting back with promises of lawsuits and heated rhetoric, including a shot from one GOP governor who blasted what he called Obama's "nanny nation approach" to government.

Republicans across the country are specifically challenging the mandate in the health care bill that requires every individual to have health insurance, charging that it is unconstitutional.

The individual mandate is an "unprecedented overreach by the federal government forcing individual citizens to buy a good or a service for no other reason then they happen to be alive or a person," Republican governor of Minnesota Tim Pawlenty said today on "Good Morning America."

Pawlenty said he sent a letter to Minnesota's Democratic attorney general arguing against the constitutionality of the mandate.

"They've taken it to this big, federalized, bureaucratic, government-run, kind of nanny nation approach," Pawlenty said. "I don't think defending the Constitution and individual's rights under the Constitution, and the relationship between states and the federal government under the Constitution is a frivolous matter."

Twelve state attorneys general, all of whom are Republican, have already filed suits to block the health care bill on the grounds that its requirement that everyone have health insurance is unconstitutional. Four state legislatures have already passed laws blocking the bill. On Wednesday, Virginia's GOP Gov. Bob McDonnell will sign the bill into the state's law, making it illegal for the federal government to require Americans to purchase health insurance.

Senior White House adviser David 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."

Watch live coverage of President Obama signing the health care bill at 11:15 a.m. ET on ABC News network or streamed live on ABCNews.com.

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.

Like many of his GOP counterparts, Pawlenty assailed the partisan nature of the health care bill. The legislation did not garner one single Republican "yes" vote in the House, which passed the bill Sunday night.

"There were 10 or 15 really good reforms that both sides could've agreed on," Pawlenty said. "They [Democrats] were more interested in achieving that ideological or political goal rather than working with Republicans to get something done."

Republicans are regrouping and gearing up to use the health care bill against their Democratic opponents in November's midterm elections. Ads blasting Democrats who were going to vote "yes" for the health care bill filled the airwaves well before the bill was even passed.

The Obama administration, however, believes the passage of the health care bill will actually help Democrats in the midterm elections.

"I think the heavy political lift would've been is if this bill went down," Axelrod said. "The reality of this bill is so much different than the caricature they've [Republicans and insurance companies] painted."

As the two parties prep for tight races across the country, Democrats are likely to spin the argument in a way that reflects those who voted against the bill are voting against insurance reforms that would benefit Americans, such as the removal of lifetime caps on coverage or denying coverage based on pre-existing conditions.

"Ultimately this is not about the politics of November. It's about the security of Americans now and for future generations," Axelrod said. "But I also think the politics will work out much better because we did the right thing. ... Every Democrat who campaigns on this will be able to campaign proudly."

After signing the bill, the president made remarks at the Department of Interior in what was mainly a celebratory event. In the audience were lawmakers who voted for the bill, and people whose stories the president has used in the long fight to get the bill passed.

President Obama to Sign Health Care Bill

Even after the president signs the sweeping health care legislation into law this morning, the work on health care is not over. Later this week, the president will return to the stump in Iowa to explain to the public how changes in the health care system will affect them.

The White House picked Iowa City because Obama delivered his first major speech on health care reform as a presidential candidate at the University of Iowa May 29, 2007.

The Senate also has to pass "fixes" to the bill, and Democrats are gearing up for a spate of procedural face-offs with Republicans. Sen. Jim DeMint, R-S.C., and Rep. Steve King, R-Iowa, introduced bills Monday to repeal the health care bill, and GOP lawmakers are vowing to fight the bill tooth and nail.

Some Republicans say their party made a mistake by not making more of an effort at bipartisanship, now that the bill is becoming law.

"A lot of the things Republicans said are going to be discredited. It is going to be a very painful and difficult situation for Republicans to work their way out of," said David Frum, a former speechwriter for President George W. Bush who is now a resident fellow at the conservative American Enterprise Institute.

Frum dubbed the passage of the health care bill as the GOP's Waterloo.

"If you lose something as important as this, and you pick up some seats in 2010, great, maybe you lose them in 2014," Frum said. "This bill will still be there. This bill will still be there forever."

The Congressional Budget Office predicted the bill would cost $938 billion -- mainly through a mix of tax increases and reduction in Medicare spending -- and would reduce the federal deficit by $142 billion in the first 10 years. The health care bill would extend insurance to 32 million more Americans.

Some components of the health care bill will take effect right away, including helping older Americans pay for prescription drugs and preventing insurance companies from denying coverage to children based on pre-existing conditions. Others, such as the individual mandate and more stringent regulations on insurance companies barring them from placing lifetime caps on coverage, or denying adults based on pre-existing conditions, won't take effect until 2014.

ABC News' Jake Tapper contributed to this report.