HARRISBURG — Gov. Tom Wolf’s administration and its allies worked through the day Thursday to sway enough rank-and-file House Republicans behind a $1 billion-plus tax increase to override opposition from House GOP leaders and end the state government’s 5½-month budget stalemate.

House Republicans reported that Wolf had been calling rank-and-file members in an effort to secure support. The activity came a day after leaders of the huge House Republican majority moved decisively to pin responsibility on Wolf to scrape up support in the chamber, one week shy of the modern-day Pennsylvania record for a budget standoff.

House Speaker Mike Turzai’s office said Thursday evening there had been no word from the governor. That was hours after the 12:30 p.m. deadline Turzai, R-Allegheny, had set for the Democratic governor to show whether he could assemble enough votes to move the tax package through the chamber.

Turzai’s office said he was in touch with Senate leaders about passing a short-term spending bill to keep state government operating, while Wolf’s office professed confidence that the governor would prevail.

“We are confident that we will have the support to pass this final budget,” Wolf’s press secretary Jeff Sheridan said Thursday night.

Wolf stayed out of sight Thursday, and Sheridan said the governor’s office had set no internal deadline to find the support necessary in the House. Turzai’s spokesman Jay Ostrich could not say whether the speaker would still allow a floor vote on a tax bill after the afternoon deadline.

Wolf, the Republican-controlled Senate and House Democrats have continued to back a $30.8 billion spending plan — a 6 percent spending increase — and an accompanying $1 billion-plus tax increase that has not been written into legislation.

The details of the tax plan continued to evolve Thursday. Wolf has demanded a tax increase to help wipe out deep public school funding cuts in 2011 while meeting counties’ requests for an increase in social services aid and narrowing a long-term budget deficit.

Senate leaders say they believe it can pass the Senate, and Senate Republican majority leaders signed on in exchange for Wolf’s support for legislation they’ve long sought to overhaul public pension benefits.

Wolf and House Minority Leader Frank Dermody, D-Allegheny, have downplayed Turzai’s 24-hour ultimatum, while rank-and-file House Republicans said it would be a challenge to persuade 20 or 30 of them to support the tax increase.

Pressure is mounting. Cash-strapped school districts are getting slapped with potentially crippling credit downgrades, social service agencies are laying off workers and state-subsidized prekindergarten programs are closing to hundreds of children of low-income families.