HARRISBURG — Democratic Gov. Tom Wolf on Tuesday said he was optimistic the Republican-controlled Legislature can produce a deal to patch a projected $2.2 billion budget gap in the coming days and end a nearly three-month stalemate.

Lawmakers authorized nearly $32 billion in spending on June 30 and have grappled ever since with how to fully fund it.

Wolf said he believes leaders of the House and Senate Republican majorities are on board with getting a deal done and signed by Oct. 1, before Pennsylvania’s battered credit rating gets another downgrade and he must delay more payments for lack of cash.

There is a lot of ground to cover before then.

[naviga:h3]CALLING IT A TAX INCREASE[/naviga:h3]

Wolf and the lawmakers who back a tax increase to help prop up Pennsylvania’s finances shy away from using the words “tax increase.” Instead, they try to use the term “recurring revenue” to refer to a new source of money that provides a reliable cash infusion every year — such as a tax increase.

The Senate, backed by Wolf, passed a roughly $550 million tax package that hit Marcellus Shale natural gas production; electric, natural gas and telephone utility customers; and sales through online marketplaces like Amazon and eBay.

The House rejected any sort of tax increase when it passed its plan. Instead, it wants to siphon about $630 million from accounts for environmental protection, mass transit and other programs explicitly created by lawmakers and given their own source of dedicated funding.

Wolf opposes that plan, and Senate Republicans say just $140 million of that amount is actually available and not otherwise committed to a project.

[naviga:h3]CALLING IT BORROWING[/naviga:h3]

In July, the Senate backed a revenue package based on borrowing $1.3 billion in a securitization arrangement, to be paid back over 20 or 30 years.

House Republicans, however, pushed back on that concept and instead passed a revenue plan that relies heavily on what they call the $1 billion “sale” of a state “asset.”

What that really means is borrowing $1 billion upfront in return for giving the lowest bidder — an investment bank or hedge fund, perhaps — the rights to a certain slice of state revenue for up to 10 years.

Senate Republicans, Democratic lawmakers and public finance professionals say such a transaction is nothing more than borrowing and would likely carry a higher effective interest rate even than a traditional securitization agreement because it shifts some risk to the lender.

[naviga:h3]GAMBLING WITH GAMING[/naviga:h3]

House and Senate leaders seem to agree any revenue package can rely on at least $200 million in one-time license fees from what they call “gaming.” That means counting on another expansion of casino-style gambling in the nation’s No. 2 commercial casino state, an expansion that lawmakers haven’t even approved.

Wolf and lawmakers already counted $100 million in fees toward last year’s budget from some sort of future casino gambling expansion. They were unable to agree on legislation to do it.

[naviga:h3]THAT $2 BILLION CLAIM[/naviga:h3]

Wolf on Tuesday said he’s cutting “over $2 billion to streamline government,” a claim he began making in February when he proposed a budget for this fiscal year. However, Wolf’s definition of cuts and streamlining is a broad one.

It includes perhaps hundreds of millions of dollars in cost avoidances that might have materialized anyway, such as revisions in future cost projections for medical care under Medicaid and hundreds of millions of dollars in transfers from a workers’ compensation fund and a nonprofit organization created by state law in 2002 to offer medical malpractice insurance.