PHOENIX — Gov. Jan Brewer is backing away from her demand that a new state budget include a temporary tax hike or face certain veto.

Brewer said Wednesday the message she has for lawmakers is that “as a last resort, a temporary tax increase might be required.’’ Potentially more significant, Brewer said she might accept a budget that does not include new revenues, even if it means having to make deeper cuts.

The comments are in sharp contrast to the message the governor has been delivering around the state ever since she announced her five-point plan two months ago to balance the budget. The fifth point of that plan is a temporary tax — perhaps three or four years — to raise $1 billion a year.

But Brewer has been unable to get much traction with her fellow Republicans who control the Legislature. Not only does she lack the necessary votes for a tax hike, lawmakers are balking at even putting the question to voters.

In fact, a $2.7 billion fix to the budget adopted on party lines just two days ago by the House Appropriations Committee contains no new state taxes, though it does tap money already raised by cities, counties and schools.

That proposal includes sharp cuts to K-12 education, larger than the ones imposed just three months ago to balance the current year’s budget. Brewer, who two months ago said she did not want the education system “decimated,’’ said Wednesday she is open to further reductions.

“I think we’re going to have to do more cutting,’’ she said. And Brewer said she is now fully engaged in negotiations with Senate President Bob Burns and House Speaker Kirk Adams, both adamant foes of any tax hike.

Brewer insisted she has not changed her position. And her March 4 speech to lawmakers asking them to hike taxes does use the words “very last resort.’’

But the governor also told lawmakers she would not ask “if I did not firmly and confidently believe that it is absolutely necessary.’’

Since then, in speeches and interviews, Brewer has repeated her argument that bridging next year’s the $3 billion gap between spending and revenues without a tax hike is unacceptable.

In March, for example, she told an audience of business leaders that trying to balance the budget without more income would require making cuts that would damage the state.

“I am not going to stand by and allow our education system, whether it be K through 12 or universities, be decimated because of the problem that we’re facing,’’ she said at the time. She even defended the plan amid questions about her tax-hike proposal harming the Republican Party.

“I have got to have the courage, you all have got to have the courage, to do what’s right to turn it around,’’ she told her audience. And she said those who think they can solve the financial mess without higher taxes don’t have “all the information’’ she does.

Last month, Brewer attacked plans by Republican legislative leaders to borrow money rather raise taxes.

“Funny math just doesn’t work,’’ the governor said of the idea. “It doesn’t work in your home budget, it doesn’t work in government budgets, and it doesn’t work in business budgets.’’

And Brewer, in a more recent interview, said her decision to push for tax hikes was difficult, “knowing that was truly the solution.’’

“It’s so obvious,’’ she said. “There’s no other way.’’

Gubernatorial press aide Paul Senseman said late Wednesday while Brewer is open to approving a budget without a tax hike, she doesn’t see that happening.

“She has not wavered on bit in her belief that it will be necessary,’’ he said. And Senseman said that, at least to date, Brewer has not seen any proposal from the Legislature that she could sign.

Senseman said that doesn’t mean a budget plan without a tax hike is impossible.

“We always are eternally optimistic that something is going to change dramatically,’’ he said. But Senseman said the financial outlook to date has only gotten worse since Brewer’s original March 4 speech.

It would take a nearly impossible two-thirds vote of both the House and Senate to hike taxes. That leaves the possibility of sending the issue to voters, a move that would require only a simple majority.

But it remains unclear whether voters support what the governor wants to do.

One survey showed two thirds find the plan at least somewhat acceptable if the funds “would be dedicated towards maintaining 2010 spending levels for K12 education, universities, community college and health care for the poor.’’

Another poll which asked simply whether people favored a tax hike to balance the budget found only 27 percent in support.

And a third, asking voters to choose between a freeze in state spending or a tax hike, found only 43 percent favoring higher taxes.