PHOENIX — Legislative Republicans are preparing a budget for next year that involves no new taxes, a move that could court Jan Brewer’s first veto.

Senate President Bob Burns, R-Peoria, said Monday that GOP lawmakers already have come up with at least $2.5 billion in solutions to dealing with the anticipated $3 billion gap next budget year between revenues and expenses. Senate Majority Leader Chuck Gray, R-Mesa, said that encompasses spending cuts, use of stimulus dollars and some one-time solutions like selling off or mortgaging state buildings, including prisons.

They refused to provide details, saying they will make the plan public only when they have identified the last $400 million to $500 million in fixes.

But what will not be in the package, both said, is any hint of Brewer’s call earlier this month for a temporary tax hike — up to three years — to raise $1 billion a year.

Gubernatorial press aide Paul Senseman said his boss remains adamant that any plan has to be “balanced.’’ And that, he said, means not relying overly on cutting spending or one-time “gimmicks.’’

Gray insisted that Brewer told him that she would sign a budget without higher taxes.

Senseman, however, said the Republicans are misinterpreting Brewer’s demand for a “comprehensive solution’’ to the state’s budget woes. And somewhere in there — if not immediately — the state will need more dollars.

“There are certainly mechanisms and ways to take a snapshot of 2010 and bandage something together,’’ Senseman said. He said, though, Brewer has made it clear she wants a long-term look “so we know how the state’s actions this year will impact into the future.’’

Brewer is projecting that the gap between spending and income will last at least until 2012, with some estimates putting the deficit that year in the $4 billion range. Senseman said the governor wants to see a plan that makes up at least some of that gap — she is figuring $1 million a year — with additional revenues.

At this point, both sides are digging in.

Gray said Monday that Republican leaders subscribe to the theory that higher taxes, in any form, will hurt the efforts to revive the economy. He said that belief is buttressed by comments made by Arizona State University professor Edward Prescott who said that when things are taxed, people produce less of it.

“So when we hear talk about a tax increase, we’re taxing the productivity of our economy,’’ Gray said. “If you have less productivity, you have less income.’’

Senseman said the governor shares the concerns about the effect of taxes. But he said the depth of the state’s economic woes — which Brewer repeatedly tells audiences that she inherited from Janet Napolitano — requires a more complex solution.

“It has to be balanced in the sense that it’s not overly reliant on one-time fixes,’’ Senseman said, where the state simply papers over the deficit with money that will be available just once. “And it can’t be overly reliant on cuts.’’

Gray said even President Obama realizes that taxes during a recession don’t help the economy.

That, however, is not entirely true: The president has proposed changing the tax code to limit deductions for the highest wage earners — those making more than $250,000 a year — as a method of paying for some of his reforms.