The Supreme Court's 5-4 decision, which largely upheld the healthcare act, allows states to opt out of the Medicaid expansion without losing all federal funding they receive for Medicaid, as they would have under the original healthcare legislation.
The Republican governors -- Rick Scott of Florida, Nikki Haley of South Carolina, Scott Walker of Wisconsin and Bobby Jindal of Louisiana -- also said they have decided against setting up a state-based health insurance marketplace, CBS News reported.
The healthcare law stipulates that if states don't set up such an "exchange" by 2014, the U.S. Department of Health and Human Services will do it for them.
Scott explained the state's decision to opt out of the Medicaid expansion and the exchange in a statement Sunday.
"Floridians are interested in jobs and economic growth, a quality education for their children and keeping the cost of living low," Scott said. "Neither of these major provisions in Obamacare will achieve those goals, and since Florida is legally allowed to opt out, that's the right decision for our citizens."
The act would open Medicaid in 2014 to anyone with an income under 138 percent of the federal poverty line, if their states have agreed with the expansion.
If a state opts out, citizens with incomes above 100 percent of the poverty line would be eligible for tax credits from the federal government to get insurance, CBS News said. But those below that income would be the responsibility of the state.
The Congressional Budget Office has said the expansion of Medicaid was expected to make healthcare coverage available to 16 million more people -- nearly half the 31 million expected to get insurance under the act.
Some healthcare experts noted the federal government is covering most of the cost of the expansion. From 2014-16, the federal government is to pay the entire cost of the expansion. Beginning in 2017, states would contribute, but never pay more than 10 percent of the cost of the expansion.
"A governor would be walking away from millions, in some cases billions of federal dollars" by opting out, Tim Jost, a consumer advocate and professor of health law at Washington and Lee University, told CBSNews.com.
And numerous citizens would be left without healthcare.
Scott said Florida couldn't afford the Medicaid expansion, which he said would eventually cost the state $1.9 billion. He also said the state provides assistance for families with incomes up to 133 percent of the poverty line and that the Florida KidCare program insures children.
"I think the chief justice basically said this is up to the American people to decide. We've got one last chance here to defeat Obamacare. We can do that in the November election," the Kentucky Republican told "Fox News Sunday."
He called the U.S. Senate races in November "a referendum on this job-killing healthcare tax-increasing measure."
McConnell said the Patient Protection and Affordable Care Act, which the Senate passed in December 2009 and the House approved in March 2010, was "the single worst piece of legislation that has been passed, certainly in modern times."
Conservative Chief Justice John Roberts wrote for the majority the law's key provision -- the so-called individual mandate requiring all Americans to maintain minimal essential health-insurance coverage or pay a fine, unless exempted for religious beliefs or financial hardship -- was constitutional because it amounted to a tax Congress has a right to impose.
Likely GOP presidential nominee Mitt Romney believes the individual mandate is a penalty not a tax, Romney spokesman Eric Fehrnstrom said on MSNBC Monday. That view doesn't square with that of congressional Republicans, who have called the individual mandate a tax, not a penalty, agreeing with the Supreme Court's majority ruling.
"The governor disagreed with the ruling of the court; he agreed with the dissent that was written by Justice [Antonin] Scalia, that very clearly said that the mandate was not a tax," Fehrnstrom said.
As Massachusetts governor, Romney instituted a healthcare law that included an individual mandate and at the time, called it a penalty or fine, not a tax.
"The governor believes what we put in place in Massachusetts was a penalty and he disagrees with the court's ruling that the mandate was a tax," Fehrnstrom said Monday.
McConnell twice refused to say what Republicans would do to extend healthcare coverage to 30 million uninsured Americans, who would be covered under the Affordable Care Act, if they controlled the White House and Congress and then repealed and replaced the law.
Of the healthcare reform law's requirement that people can't be denied coverage due to pre-existing conditions, McConnell said Republicans would encourage states to prohibit insurers from denying coverage on that basis.
White House Chief of Staff Jack Lew told the program Americans wanted "the divisive debate on healthcare to stop."
"I actually think the American people want us to focus on the economy, on creating jobs and moving forward," he said.
The Republican-controlled House has scheduled a vote on a measure to overturn the healthcare-reform law in one week.
The vote is widely seen as symbolic since Democrats control the Senate. But congressional aides say the vote will put lawmakers on record for the fall political campaign.