HARTFORD — Speaker of the House Joe Aresimowicz on Friday planned to call for a special session of the House of Representatives as soon as Tuesday.

But whether he is limited to dealing with an issue over federal reimbursements for state hospitals — or he can call a quick vote that could kill an attempt to override Gov. Dannel P. Malloy’s veto of a Republican-based budget — might be up for legal interpretation.

“We’ve asked members to check their availability and hold a number of dates for potential House sessions in the coming weeks,” Aresimowicz said in a statement. “When ready, we need to act quickly on the hospital and federal funds issue, there has to be a session to consider the governor’s veto, and in the absence of an override we need to come to a final budget agreement that will become law.”

Republicans say the earliest a veto-override could occur is Tuesday, Oct. 10, in accordance with the state Constitution.

Article III of the Constitution says in part: “If any bill passed by any regular or special session or any appropriation item ... has been disapproved by the governor prior to its adjournment, and has not been reconsidered by the assembly, or is so disapproved after such adjournment, the secretary of the state shall reconvene the general assembly on the second Monday” after Malloy’s veto.

That would mean Oct. 10, Tuesday, following the Columbus Day holiday, according to Republicans, who are trying to build momentum over the next week in attempt to win the 101 votes in the House and 24 in the Senate needed to override.

But since the special session was not adjourned, does that mean Aresimowicz could call for the override vote before the 10th?

It was too soon to tell late Friday afternoon. The next bipartisan leadership meeting with Malloy has been scheduled for late Monday afternoon.

The budget bill passed the Senate 21-15, with three Democrats and 77-73 in the House, with five Democrats. At this point, with opposition from Aresimowicz and Senate President Pro Tempore Martin M. Looney, an override seems unlikely.

Kelly Donnelly, Malloy’s spokesman, said Friday that the governor appreciates the speaker’s attention to organizing the House for potential votes.

“As the Governor stated in his veto message, the urgency to work together cannot be overstated,” Donnelly said. “The GOP-backed budget is unbalanced, unsustainable and unwise — making it one that deserved to be vetoed and one that should not garner enough votes for that veto to be overridden. We remain committed to working with leaders of all four caucuses to arrive at a fair, balanced, and responsible biennial budget that moves the state forward in the right direction.”

Capitol budget staff has been in days of negotiations with the Connecticut Hospital Association over $70 million in federal reimbursement to state hospitals. Malloy wants to link the reimbursement to a pending lawsuit the hospitals filed over the state tax on them. The CHA has been reluctant to agree to a settlement.

Earlier this week a vote on Thursday or Friday seemed possible, but the negotiations with the CHA prompted lawmakers to back away, for now.

kdixon@ctpost.com Twitter: @KenDixonCT