HARRISBURG — Leaders of the Pennsylvania Legislature’s Republican majorities will allow a floor vote on a budget package that includes an income or sales tax increase if Democrats can secure enough support to pass it, officials said Friday.

House Minority Whip Mike Hanna, D-Clinton, said Democrats are actively pursuing the avenue in a bid to break a nearly three-month-old budget stalemate. Republicans opened the door to such a floor vote during a closed-door meeting Thursday with Democratic Gov. Tom Wolf.

“This is an interesting challenge that they’ve issued,” Hanna said. “‘If you guys think you have the votes, go get them and we’ll run them.”’

Until Thursday, House Majority Leader Dave Reed, R-Indiana, and Senate Majority Leader Jake Corman, R-Centre, had said they would not agree to a budget package that included an increase in the sales tax or income tax. That refusal has created a significant obstacle to Wolf’s pursuit of a multibillion-dollar tax increase that he says is necessary to wipe out the GOP’s funding cuts for schools and human services enacted under Wolf’s Republican predecessor, Tom Corbett, and eliminate the deficit.

Reed and Corman do not believe Democratic minority leaders can win over enough Republicans or, for that matter, Democrats.

“We haven’t gotten any indication that (the support) would be there and we’ve heard from Democrats that it’s not necessarily there,” Corman’s spokeswoman, Jennifer Kocher, said Friday.

In a Friday e-mail message to rank-and-file House Republicans, Reed echoed that sentiment.

“As I have reiterated to them time and again, I believe the 102 votes needed for any increase to the income or sales taxes only exist if all of the dollars are dedicated to property tax reform/elimination — not for additional state spending,” Reed wrote.

In the 203-seat House, Democrats would need 18 Republicans to get to a simple majority of 102 votes, assuming all 84 Democrats are on board. There is one vacancy in the 50-seat Senate, meaning Democratic leaders would need support from at least six Republicans, assuming all 19 Democrats are on board.

“Even if we have 102 votes, if they don’t agree to put it up for a vote, we can’t get there,” Hanna said. “So yesterday was the first time they gave any indication that if we thought we had the votes for a package that they’d put it up for a vote.”

Republicans have flatly rejected Wolf’s $31.6 billion budget proposal, saying it would require the biggest tax increase in the state’s history.