The Legislature's Democratic leaders said they had already agreed to a tax cut and accused the governor of just trying to win more national attention.
Speaking on Fox and Friends, Christie told of rejecting legislative Democrats' $800 million income-tax increase, but did not mention that the increase was intended only for people making more than $1 million or that the Legislature also had adopted a tax-cut plan for most residents tied to the property tax.
Christie, who has criticized the U.S. Supreme Court's ruling last week upholding the federal health insurance overhaul, said again that the ruling was wrong.
He said he was weighing whether it would be less expensive for the state to let the federal government set up New Jersey's health exchange rather than have the state set one up itself. He said he would choose the more cost-effective option.
He also praised the part of last week's ruling that reduces the federal government's ability to force states to expand Medicaid to include people with incomes up to 133 percent of the poverty level.
"Medicaid is pretty well expanded in our state already," he said. "I don't think there's a lot for us to do in New Jersey."
In New Jersey, people with children are eligible for subsidized health coverage even if they make up to 350 percent of the poverty rate - or nearly $81,000 for a family of four.
Various programs also serve childless adults with different income limits. But participants who are not pregnant, blind, or disabled must make less than the poverty level.
Later in the morning, on CNBC's Squawk Box, Christie said the Obama administration should give more Medicaid money to states with no strings attached, rather than specifying that each state should expand eligibility to the same level.
"What works in New Jersey, I suspect, would be very different from Montana," Christie said.