Republican lawmakers are turning up the heat on Gov. Jon Huntsman Jr., pressing him to double up on budget cuts for next year and to quickly convene a special session to address this year's $350 million shortfall.

"We would still like to have a special session," Speaker-elect Dave Clark, R-Santa Clara, said Monday, following an all-day House Republican caucus.

In September, Huntsman called a special session so the Legislature could fill a $280 million budget hole. The latest revenue numbers show another $350 million gap, and Clark said lawmakers want to "legislatively take on that responsibility."

"If it was good enough the first time, we'd like to be doing it a second time," Clark said.

But Huntsman, who is the only one who can call a special session, isn't budging.

"I think we're close enough to the regular session," scheduled to start Jan. 26, Huntsman said in an interview Friday. "We can look forward to that." His position has not changed, his spokeswoman, Lisa Roskelley, said Monday.

Huntsman said he is confident there will be a sizeable federal stimulus package passed soon, which could send billions of dollars to the states for transportation and construction projects. Until that package takes shape, he has said it would not be productive to hold a special session now.

State agencies have already been asked to cut their spending by 1.5 percent, with changes to Medicaid eligibility, payments to county jails that house prison inmates, and drug and sex offender treatment programs all taking a hit.

But Clark said that the state is spending about $450 million a month. At that rate, the further into the fiscal year it gets, the harder it will be to balance the numbers, which is required by the Utah Constitution.

Meantime, Republicans in both the House and Senate have agreed on a 15 percent budget reduction for the coming year, slashing more than $1 billion from the budget they approved just last March. Huntsman is proposing a 7 percent cut from the post-special session budget levels.

"We're here today looking at a $1 billion reduction in what we spend in the state," Clark said. "This is an unprecedented time. We don't have a historic benchmark to try to figure out billion-dollar-plus cuts in the State of Utah."

Senators agreed to the 15 percent reduction during their caucus meeting Saturday afternoon. State agencies have been asked to provide legislators a snapshot of what it would take to meet those targets.

During their caucus, House Republicans also agreed -- generally at least -- on some broad areas for ethics reform, but did commit to specific policies. Rep. John Dougall, R-Highland, the incoming chairman of the House Ethics Committee, said there is an appetite for prohibiting the personal use of campaign funds, limits on meals and gifts from lobbyists, and a "cooling-off" period during which time former lawmakers would be prohibited from lobbying the Legislature.