Democratic New York Gov. Andrew Cuomo, for example, wants to tap a surplus to roll back recent tax hikes, despite other Democrats' ideas for new spending. In Louisiana, Republican Gov. Bobby Jindal wants to steer the surplus to education and health care.
The National Association of State Budget Officers projects that almost all states will see "fairly decent surpluses" in their 2014 budgets. For some, it may be the first extra cash since before the recession began in late 2007. In many states, the surpluses coincide with elections that mark the first opportunity for officials to be judged on the results of their economic policies.
(Read more: Identity thieves gear up to steal your tax refund)
Voters in November will choose 36 governors and more than 6,000 state legislators in what amounts to a referendum on whether they want to continue the single-party dominance that currently exists in three-fourths of state capitols.
"I think this election cycle will tell us a lot about whether or not we're going to have better fiscal-management officials in charge, or whether we're going to go back to business as usual, which is if the revenue comes in, let's figure out a way to spend it," said Ross DeVol, chief researcher at the Milken Institute, an economic think tank in Santa Monica, Calif.
In California, once the epitome of busted budgets, a resurgent technology sector and recent temporary tax increases have generated forecasts of a $3.2 billion budget surplus. Democratic Gov. Jerry Brown wants some increased spending but also to pay down debts and rebuild a rainy day fund.
"It isn't time to just embark on a raft of new initiatives," Brown warned.
Yet the pressure for more spending already is building among Democrats who control the Legislature. Some want to reverse cuts for welfare programs or launch a new preschool initiative.
In Republican-led Louisiana, Jindal's desire to use the surplus for education and health care will be competing with other GOP calls for highway construction and restocking a state reserve fund.
Some states with surpluses are not necessarily in great fiscal shape. They still have underfunded pension systems, shortfalls in school funding formulas and infrastructure needs that far exceed their available dollars for roads and bridges.
Yet numerous governors and lawmakers are citing the surpluses as a reason to cut taxes, including some in GOP states that already have shaved hundreds of millions of dollars off taxes in recent years.
The budget director for Republican Michigan Gov. Rick Snyder has predicted that an additional tax cut is "inevitable" in light of a roughly $1 billion surplus. Yet Snyder first wants to put more money into early childhood education.
"Then to the degree that there are some resources left, it's a fair question: What can go in the rainy day fund or what can be given back to taxpayers?" Snyder said in an interview with The Associated Press.
Wisconsin Gov. Scott Walker's fiscal record will be put to the test this year. The Republican pledged while campaigning in 2010 to create 250,000 jobs, but he is less than halfway to that mark. Tax cuts could help his re-election appeal. Walker signed about $750 million of tax reductions last year and could seek more.
Big tax cuts also are on the agenda in Florida and Missouri, where budget surpluses are expected.
"If we put a tax-reduction package in place, I believe long-term we're going to grow our budget and grow our economy," Missouri Republican House Speaker Tim Jones said.
Some Democratic governors facing re-election also are proposing to roll back recent tax hikes.
Democratic Minnesota Gov. Mark Dayton wants to devote half of an $825 million surplus toward cutting taxes for the middle class and repealing new taxes on business transactions. But he's already facing resistance from the Senate Democratic leader, who's not up for re-election.
Some budget analysts are urging caution. The revenue surge, they note, is driven partly by stock-market gains and other one-time factors.
(Read more: John McCain calls out congressional pork on Twitter)
"It will be quite naive to hope that the surpluses will be sustainable in the coming years," said Lucy Dadayan, senior policy analyst at the Rockefeller Institute of Government. "And it will be quite naive as a result to cut taxes or to introduce new spending programs."
—By The Associated Press