PHOENIX — At an impasse with lawmakers over a sales tax referral, Gov. Jan Brewer is now looking to supporters to take the issue to the ballot themselves — even if that delays the levy more than a year.

Brewer said Friday she understands that legislators, having wrestled with the budget now for months, are in little mood to come back again in yet another a special session this year to try to once again craft a plan that would boost state revenues to make up some of the gap between spending and income. The governor said, though, she has not given up hope that legislative support could eventually be found for her proposal to temporarily hike the state sales tax.

But Brewer said that’s not the only option.

“There are people in the community that feel maybe they’ll have to do that by initiative,’’ she said.

Trying to balance the budget without additional cash, Brewer said, is not a realistic option.

“We’ve got an $11 billion budget and we’ve got $7 billion in revenues,’’ the governor explained. “Somewhere, somehow, we’ve got to resolve it.’’

The advantage of an initiative is it bypasses the need to marshall the votes in the Legislature to refer the measure to the ballot, votes Brewer has been unable to line up, at least in the Senate.

But the trade-off is that lawmakers are legally able to schedule a special election any time they want. By contrast, the soonest an initiative could go to voters is November 2010.

“Of course, if it does wait until November, it’s not going to help us out much currently,’’ she said, what with the deficit she is trying to fix being for the fiscal year that ends June 30, 2010.

Ignoring the deficit is not an option: While the Arizona Constitution does not specifically require lawmakers to adopt a balanced budget, it does prohibit the state from going into debt for more than $350,000. That has been interpreted to mean that, by the last day of the fiscal year, the books have to be within $350,000 of being in the black.

But Brewer pointed to continued bleak revenue predictions that show Arizona could continue to have spending obligations that exceed revenues into 2014.

The governor had been counting on a special election this November, with an eye on starting to collect an extra 1 cent on the state’s 5.6 percent sales tax in January. That could bring in close to $500 million for the balance of this fiscal year.

Even with that, though, Brewer agreed to spending cuts and borrowing. But much of the difference was made up with about $1 billion in federal stimulus dollars.

That, said Brewer, makes approval of a temporary sales tax hike — even one that cannot take effect before 2011 — all the more important.

“The stimulus dollars will be gone,’’ Brewer said of future budget years. “We need that temporary revenue to bridge that gap.’’

Brewer said, though, that she is open to revenue options other than a temporary sales tax hike.

One is the idea of allowing horse and dog tracks to also operate casinos. Industry backers say a 45 percent tax on wagering could bring in more than $400 million a year.

When Brewer was running for secretary of state in 2006 she responded in a questionnaire that she believes casino gaming should be limited to reservations. By Friday, though, Brewer was taking a more equivocal position.

“That’s something that has to be fully debated and talked about,’’ she said.

But Brewer was decidedly more cool to another alternative being pushed by car dealers: Requiring those who buy cars from other individuals to pay sales taxes just as if they were making the purchase from a car lot.

“I always believed that was kind of an American thing: If you own something, you could sell it,’’ the governor said. Brewer said she views selling a car the same as having a garage sale, saying these should be exempt from taxation “unless you do it every Saturday morning.’’