HARRISBURG — In his first two years in office, Gov. Wolf lobbied for hikes in Pennsylvania's income or sales taxes to fill deep holes in the state budget. Both times, he lost the fight.

On Tuesday, he is to deliver his third annual budget proposal, this time pledging not to rely on the kind of broad-based taxes that the Republican-controlled House and Senate have made clear they won't support.

That leaves unanswered a central question: How does the governor plan to close a shortfall projected at nearly $3 billion over this year and next?

In recent weeks, Wolf has disclosed some of the steps he would take: Corrections officials say they will close the state prison in Pittsburgh, and Wolf is asking legislators to merge four state agencies -- the Departments of Aging, Drug and Alcohol Programs, Health, and Human Services -- into a single department. The governor's office has even hired consulting firm McKinsey & Co. for advice in bridging the budgetary gap.

Wolf aides promise that more is coming.

"There will be some revenues, including a [natural gas] severance tax, and some closing of loopholes and things like that," spokesman J.J. Abbott said Friday.  "But the goal was to build out a budget that relied most heavily on savings and efficiencies and cuts."

The administration has thus far kept close many of the details – including the specific dollar savings -- leaving Capitol players and spectators wondering how the figures will be balanced.

"I've approached a lot of budgets in my day; this one truly catches my interest," said Drew Crompton, the top lawyer to Senate Republicans. "If the premise is what we all think it is — and by that I mean no broad-based tax increases and a deficit that is in the ballpark of $3 billion — I am intellectually curious about how you make those two things work."

The state's budget is more than a dry fiscal exercise. It lays out most of what the Pennsylvania government will do and contribute to — from providing social services to educating schoolchildren to policing communities — in the coming year. It can dominate months of attention at the Capitol, from the governor's proposal in the first months of the year to the weeks of legislative budget hearings that follow, all typically culminating in a frenzy of negotiations and votes as the fiscal year ends June 30. Sometimes, as with Wolf's first budget, the budget stays unfinished for months longer.

But this year brings with it a politically charged undercurrent. The first-term Democratic governor will be negotiating the budget with the GOP-controlled General Assembly even as he gears up for his reelection campaign. Already, he has one Republican opponent with influence of his own over the direction of the budget: Sen. Scott Wagner, an unapologetically bombastic millionaire businessman who hails from the same York County area as the governor.

Aides said Wolf has been practicing his speech for days, and would be doing so through the weekend, making tweaks and changes.

They said he will again propose increasing state funding for K-12 education, a priority throughout his years in office, as well as workforce training. He has already declared he will call for spending $10 million on Naloxone, which treats opioid overdoses, for use across the state.

But beyond the rising costs of what the state already does, "any new investments are relatively minimal," said Sarah Galbally, Wolf's secretary of policy and planning. In the past, Wolf had argued that raising the sales or personal-income taxes was the sustainable way to meet rising costs while increasing funding for schools.  In his first budget proposal, he had advocated for using a portion of those tax hikes to fund decreases in property taxes.

This year, the savings and spending cuts Wolf will propose will total more than $1 billion, Abbott said. The governor's money-generating proposals will include a tax on natural-gas drilling, a proposal that in past years has failed to win enough support, particularly from legislators where Marcellus Shale drilling has stirred jobs and development.

But they will not include increasing tobacco taxes, leasing state alcohol-sales operations, or expanding gambling beyond a yet-to-be-approved proposal already included in the current year's budget, Galbally said.

Through midday Tuesday, attention is focused on what Wolf will propose for the fiscal year beginning July 1. But immediately afterward, that focus will shift to the response of the House and Senate.

"It's hard to say what I expect to hear, because he hasn't really given us a whole lot of information," Senate Majority Leader Jake Corman (R., Centre), said late last week. "What I hope to hear is a re-forming and restructuring of state government to save the taxpayer dollars, as opposed to looking to the taxpayers for more dollars."

House Majority Leader Dave Reed (R., Indiana), sounded a similar note.

"We're anxious to see what he's going to propose," Reed said. "Certainly we have been pleasantly surprised that he has taken a lot of the concerns that we've had as a caucus, and ideas that we've had, as far as taking the personal-income tax and sales tax off the table, and then ... the issue of restructuring and reinventing government."

Senate Minority Leader Jay Costa (D., Allegheny) said the address Tuesday is a chance for Wolf to help define the path forward.

"Instead of letting the Republicans tell him we're cutting and this is how much you're going to spend, he's going to help frame that himself," Costa said.

With President Trump now at the helm in Washington, Rep. Joe Markosek of Allegheny County, the ranking Democrat on the House Appropriations Committee, noted that the Pennsylvania budget may not be entirely under the control of state officials.

"The real wild card here is not the governor but rather what the federal government is going to do with their funding and programs," Markosek said.