Gov. Mark Dayton rolled a political hand grenade into Republican leaders' piecemeal budget solution Monday, informing them he will reject all bills until they present a complete, balanced financial package.

Dayton issued a sternly worded, three-page letter hours before the GOP-controlled House passed a tax bill that would gut aid for the state's largest cities -- a signature Republican initiative designed to kick off a week's worth of votes on budget bills that cut most state agencies.

The letter "was probably a step backward," House Majority Leader Matt Dean said Monday.

Deputy Senate Majority Leader Geoff Michel, R-Edina, took more pointed aim at the governor.

"Leadership is not writing letters," he said. "Leadership is not drawing lines in the sand."

Dayton also wants the GOP to do what other Legislatures have done -- abide by Revenue Department estimates for what each proposal will save or cost the state. He said he won't negotiate with them until they do so. Republicans last week revealed that they were basing their estimates on numbers from private business and other states.

Dayton also served notice that he will reject any budget bill sprinkled with what he deems to be divisive policy provisions. If he rejects bills he considers flawed, he said, "those delays will be the Legislature's responsibility, not mine."

The governor's letter cast a cloud of uncertainty before the House approved the tax bill 73-59. The bill dramatically reduces aid to Minneapolis, St. Paul and Duluth, and imposes a host of other aid reductions that budget officials estimate could cause property taxes to rise by more than $1 billion.

The proposal also includes across-the-board income tax cuts, which would go largely to Minnesota's wealthiest residents. The poorest 10 percent of Minnesotans would get an additional 87 cents a year from their income tax cut, while the wealthiest would receive an average of $415 a year.

"What is not in this bill is job-killing tax increases that will break the back of this recovery and break the back of this state," Dean said. "We need to cut taxes, and this is what we did. That's a balanced approach to move forward."

Republicans are poised to approve the budget bills earlier than any time in recent years, but with gaping uncertainty about many of the numbers. Facing questions about their budget assumptions last week, Republican leaders raised doubts about the hundreds of fiscal analyses done by non-partisan state budget staffers that showed that many of the GOP's proposed cuts don't save nearly as much as Republicans had hoped.

Such fiscal notes, as they're called, have always been a controversial but bedrock part of the budget process. While state law does not require them, they ensure that everybody is working from the same set of numbers.

The governor's office spends months building its budget outline, so when legislators take their turn, the state analysts often use much of that work to build their estimates.

The warring over budget estimates gets most heated when the administration and the Legislature are controlled by different parties, as is the case now.

Late last week, GOP leaders said they favored their own estimates, drawn from private industry and other states, above those provided by state budget officials.

Facing criticism from Dayton and other Democrats, Republicans rolled out video showing DFLers in 2008 questioning the soundness of Republican Gov. Tim Pawlenty's numbers.

One video clip showed Sen. LeRoy Stumpf, DFL-Plummer, saying that "agencies will, I think, doctor fiscal notes if they, you know, want to tilt it toward a certain policy, or away from a certain policy."

Sen. Larry Pogemiller, DFL-Minneapolis, a frequent critic of Pawlenty's budget, said Democrats regularly questioned assumptions in the financial estimates. But "there's always a general acceptance -- whether you like them or not -- that these are the facts that you have to work with," he said.

Even the best financial estimates require a good bit of guess work.

"Who's to say they are right?" asked Tom Hanson, former commissioner of Management and Budget under Pawlenty.

Perhaps, he said, Republicans are proposing new solutions that can't easily be calculated by budget officials tied to an old way of doing things.

Republicans have much at stake in getting the numbers right. An error could force them to come back next year and tear open the budget to make more cuts.

The sweeping education spending bill up for a vote Tuesday contains a plethora of policy provisions that Dayton will insist be removed.

The 118-page bill would bar teachers from striking, virtually eliminate tenure and create a statewide teacher evaluation system. It resurrects a debate over "vouchers" that provide poor Minnesotans at low-performing schools money for private schools. It limits contract negotiations to summer vacation months and creates an A through F system for grading Minnesota schools.

"I will not sign ... bills that include policies to which I have not agreed, which I oppose," Dayton wrote.

Eric Roper, Mike Kaszuba and University of Minnesota intern McKenzie Martin contributed to this report. Baird Helgeson • 651-222-1288