In the party's weekly radio and Internet address, McDonnell criticized the Democratic administration for opposing an appeal of the year-old measure to the high court.
"The very same administration that was in such a rush to pass the bill is in no hurry to find out if it's legal," he said.
Among the most contentious issues in the bill is the shifting of healthcare costs to states from the federal government.
"The more spending required for Medicaid entitlements, the less money available for roads, schools, law enforcement and higher education," the governor said. "Here in the states, we have to balance our budgets. We can't print money, and we have strict debt limits, so we have to live within our means."
He said his state now spends 21 percent of its annual budget on Medicaid, but under the current law, those costs would rise to 26 percent by 2016.