Senate President Thomas V. Mike Miller Jr., left, Gov. Martin O'Malley and House Speaker Michael E. Busch at a hearing in 2011. (Patrick Semansky/AP)

Senate President Thomas V. Mike Miller Jr. (D-Calvert) and House Speaker Michael E. Busch (D-Anne Arundel) plan to meet with Gov. Martin O’Malley (D) on Tuesday morning to discuss cleaning up the messy end of the 90-day legislative session.

Lawmakers adjourned at midnight April 9 without passing an agreed-upon tax package, a failure that will trigger more than $500 million in cuts to education and other planned spending if they do not reconvene.

The meeting, confirmed by State House aides Friday, will be the first time Busch and Miller have met face-to-face since an awkward bill-signing ceremony on the day after the session ended.

Legislative leaders have also sparred over the role a gambling bill played in the demise of the final night of the session. The bill called for a public referendum on a Prince George’s County casino and allowing table games and Maryland’s five existing slots locations.

On Friday, Miller sent a letter to O’Malley and Busch saying he has not and will not “connect” the issue of gaming to the budget.

“But I will state that I remain frustrated,” Miller wrote. “It is foolish to deny Maryland locations the ability to offer table games just like our neighboring states and to refuse to permit a sixth site which we know will be the best location on the East Coast with most of the estimated revenues coming from out-of-state visitors.”

Miller’s letter also proposed a modification to one of two revenue bills that will need to be passed to offset more than $500 million in spending cuts.

Busch declined to comment on Miller’s letter, but an aide said the issues raised in his letter will be among the topics of conversation Tuesday.

In a letter back to Miller, O’Malley said: “I really appreciate your willingness to complete the General Assembly’s budget agreement for fiscal year 2013. I’ve never known a session to end with a perfect result, but concluding the budget would certainly be a positive step forward. ... Look forward to seeing you Tuesday with the Speaker.”