HARRISBURG - The path to resolving Pennsylvania's budget stalemate remained murky Tuesday, as Gov. Wolf and a top Senate ally appeared to double down on their long-held positions, while Republicans explored if they had the votes to enact a spending plan without the governor's signature.

In a radio interview, Wolf insisted he would not back off his calls for major changes to overcome the state's multibillion-dollar budget deficit.

"I think there's a dawning awareness that I'm not going to cave on this, I can't cave on this," he told KDKA-AM in Pittsburgh, shrugging off last week's rejection of his tax plan by the Republican-controlled House. "I'm one of 12.7 million Pennsylvanians, and we've got to have our state on a sound financial basis. That's all I want."

House members went home after last week's vote, but senators reconvened on Tuesday.

Jenn Kocher, a spokeswoman for the Senate Republicans, said caucus leaders were exploring the possibility of trying to persuade enough Democrats to break rank with Wolf to pass a veto-proof spending plan - or even just a temporary budget - to provide ailing nonprofits and school districts with cash while legislators work on a permanent accord.

State Sen. Vincent Hughes (D., Phila.) said he did not believe Democrats would support those maneuvers. He suggested that Republicans - who have rejected Wolf's call for a tax hike - come back to the table.

"They've got to realize they're not totally in charge," Hughes said.

There was no indication that leaders on either side had returned to the negotiating table. Hughes and Wolf said informal budget talks between staffers took place over the weekend and would continue this week.

In his radio interview, Wolf said that even though every Republican House member and nine of his fellow Democrats rejected his proposal, "there has to be a recognition" in the Capitol that eliminating the deficit will require more than one-term revenue solutions.

In past years' budget negotiations, "both parties have basically been complicit in having a casual approach to our finances in Pennsylvania," Wolf said. "We can't afford to do that anymore."

His plan would increase the state's personal income tax from 3.07 percent to 3.57 percent, and impose a new tax on natural gas drillers. He has proposed using the funds to close the budget deficit and send more money to schools.

With the state's spending plan more than 100 days overdue, nonprofits and school districts that rely on state aid have been without disbursements since July.

Republicans said after last week's vote that Wolf should take that rejection as a sign that there is no support for significant tax increases to support his agenda. Kocher, the Senate Republicans' spokeswoman, repeated that stance on Tuesday.

Wolf said during his interview that while he understood many agencies were suffering without cash infusions, he won't settle for a budget just for the sake of time.

"I'm holding out for a permanent benefit here, for a long-term gain," he said.