The other believes the answer should come through legalizing slot machines, combined with a handful of more modest tax increases.
That means the most likely solution may be no solution at all - a balanced budget for fiscal year that begins in July, but no headway toward closing the $1 billion gap between revenues and spending projected for just one year later.
"There's a fairly decent chance of that," said Del. Kumar P. Barve, a Montgomery County Democrat and the House majority leader. "But having put a serious tax proposal forward, there's also a chance for a serious compromise to be struck."
Negotiations are expected to begin this week, when the House and Senate leaders appoint five members each to the conference committee.
The revenue question dwarfs virtually every other piece of legislation under consideration with two weeks to go before the scheduled April 12 adjournment.
Both the House and Senate have passed $23.6 billion spending plans for next year, with relatively few differences. A combination of one-time fund transfers and other budget tricks ensure that both plans are balanced, without any need for broader revenue increases.
But the state's budget has now been balanced for three years in a row with stop-gap measures, and there are far fewer of those options left.
That is why both chambers passed legislation separate from the fiscal 2005 budget to raise money for future years: The House approved one of the largest tax increases in state history last week; the Senate has passed a slots bill for the second straight year.
Neither likes the other's ideas, which leaves the negotiators a wide gap to bridge.
Many leading lawmakers hope the speaker, governor and Senate President Thomas V. Mike Miller will find a way to hammer out a deal in the next two weeks. So far this session, the three have met once; Ehrlich and Busch have not had a meeting since their dinner last Sunday night.
"I sure would like to see Mike Busch, Mike Miller and the governor sit down together and work this out," said Del. Sheila E. Hixson, a Montgomery County Democrat and chairwoman of the House Ways and Means Committee. "But if they don't, we'll have to take this thing to conference committee. They will want slots. We'll offer taxes. And hopefully there will be a way to find something we can agree on."
That's the same type of compromise envisioned by Miller, who says he will support whatever package gets the backing of the executive and legislative branches.
"The end game has got to include slots and revenues," Miller said. "It means the speaker has to give, and the governor has to give."
So far, neither has shown much flexibility.
Ehrlich remains adamant that he will reject any version of a sales or income tax increase. Asked if any component of the House tax package approved last week was palatable, state budget secretary James C. "Chip" DiPaula Jr. said: "I'm unaware of any that are acceptable to the governor."