Markell also said a long-term deal would be better than a “three-month fix.”
Utah Gov. Gary Herbert said his state's budget could lose as much as $500 million.
States are willing to do more with less, he said, if some strings are removed.
White House press secretary Jay Carney said the session “was a good, solid meeting discussing the fiscal cliff … the shared concerns of governors that we address our fiscal challenges in a way that ensures that the economy continues to grow and create jobs.”
After meeting with the congressional leaders, Fallin said there was still “a lot of political divide between the two political parties in the House and Senate leadership about the answers to solving our challenging fiscal crisis.”
House Republicans made a proposal on Monday that would allow for $800 billion in new tax revenue over 10 years by closing loopholes and reducing deductions for upper-income taxpayers; the GOP proposal would also make cuts to Medicare and Social Security and other federal spending.
Obama has insisted that a deal include higher income tax rates on families with incomes above $250,000.