In a letter urging House leaders to make one final try at enacting a quarterly “mini-budget” before Connecticut rings out the old fiscal year at midnight Friday, Gov. Dannel P. Malloy both added to the political pressure on House Speaker Joe Aresimowicz of Berlin and tried to spread it to Rep. Themis Klarides of Derby, leader of the sizable Republican minority.

Aresimowicz, a Democrat in a first fitful term as leader of the House, has come in recent days to personify the inability of the General Assembly to address the state’s budget woes with at least a spending plan for the first three months of the new fiscal year. Senate leaders say they are ready to act; Aresimowicz says the House is not.

The speaker, who may not have sufficient votes in the closely divided House to defeat GOP amendments on major issues related to pending labor concessions, said he would not consider calling a vote on a limited budget without a pledge from Klarides for a clean vote, meaning no amendments and limited debate.

Essentially, Aresimowicz is calling for a temporary political truce in which legislators would pass a mini-budget to keep the state functioning, then resume the political battle over the larger question of what Connecticut should tax and spend in the two-year period that begins July 1.

“If it’s the mini-budget — meant to be the band-aid, not the final decision — then let’s treat it as such,” Aresimowicz said in an interview late Wednesday afternoon. “There should be no amendments, limited debate. Get in to do what we need to do, then get out. I haven’t heard that from anybody yet.”

The letter Malloy sent earlier Wednesday to Aresimowicz and Klarides publicly addresses the possibility that a number of House Democrats might be unavailable to vote Thursday, raising the question of why a legislator would have scheduled business or vacation travel in the final week of a fiscal year that was likely to arrive as this one did — without a new budget in place.

“As leaders of the House of Representatives, you could each commit to bringing a proportionate number of your members necessary to pass this measure,” Malloy wrote. “This would be a strong signal that Connecticut state government can put politics aside and work in a bipartisan fashion. It would also give us positive, bipartisan momentum toward an eventual biennial budget vote.”

The governor, a Democrat not seeking re-election in 2018 after two terms, has grown noticeably impatient with a House Democratic leadership that the administration sees as lacking a sense of urgency and an ability to ensure that Republicans share in the political price that may come from inaction.

His letter prompted an exchange of replies from Aresimowicz, Klarides and, finally, the governor’s communication director. The subtext of the missives from the governor is clear: He wants Aresimowicz to call a vote on the limited budget, challenging anyone who votes no to take responsibility for the difficulty that will follow if Connecticut goes without a budget.

In a statement, Aresimowicz indicated House leaders would work late on trying to craft a deal that could come to a vote. But in his subsequent interview with CT Mirror, he expressed doubt that a vote would go forward for reasons of substance, politics and practicality.

“I think the governor is working hard to get us into session to do what he feels is necessary,” Aresimowicz said.

But he said the formal legislative language to implement Malloy’s proposed limited budget was not delivered to the legislature until 4 p.m. Wednesday, and it typically takes 48 hours for the legislature’s Office of Fiscal Analysis to prepare a budget for a vote. Klarides was not expected to agree to a clean vote on the mini-budget.

Aresimowicz spent much of the day around a long conference table with senior staff and House Majority Leader Matt Ritter of Hartford and Reps. Toni Walker of New Haven and Jason Rojas of East Hartford, the co-chairs of the two fiscal committees, Appropriations and Finance. He said they would be looking at narrowing the governor’s mini-budget.

“We’re looking at it. We’ve reached out to the minority leader with a list of items contained within the mini-budget that we consider necessary or needed and left off the things we thought he overreached on,” Aresimowicz said. “We’re awaiting a reply from her. But that’s part of the deal with the chambers being as close as they are — that we’re all required to govern.”

At the start of the Obama presidency, Democrats in the legislature had majorities of 24-12 in the Senate and 114-37 in the House. The Senate is now tied, with Democrats’ only edge coming from the tie-breaking vote of Lt. Gov. Nancy Wyman. The Democrats’ advantage in the House has shrunk to 79-72, the smallest working majority in House history.

Malloy acknowledges that there is no consensus for how to balance a budget for the new biennium. Connecticut adopts two-year budgets in odd years, then adjusts them in even years. But Malloy has repeatedly pressed legislators to adopt a temporary fix that shrinks government and adds revenue to avoid worsening a projected shortfall of $2.3 billion in the fiscal year that begins July 1 and $2.8 billion the following year.

“I would hope that we could all agree that any action is better than no action at all,” Malloy wrote to the House leaders. “However, if you disagree, and if no action will be taken in the House before July 1, I would like to know the following: Is there an agreement between House leaders not to act on the mini-budget? If so why is operating government without a budget a more responsible path than passing the proposed mini-budget? Do you plan to have your caucuses here on Thursday or Friday ready to act if needed?”

Klarides was unavailable Wednesday for an interview, but she reacted sharply in a written statement.

“To suggest there was some agreement between House Republican leadership and the Speaker to not act is patently false,” Klarides said. “House Republicans have crafted three balanced budgets since April, one in conjunction with the Senate Republicans and two other separate proposals that accounted for continuing changes in revenue. We have repeatedly asked for votes on our budgets and stand ready to take action whenever the legislature convenes.’’

Kelly Donnelly, the governor’s communication director, issued a statement that  praised Aresimowicz for seeming to be working on a compromise and tried to hold  Klarides responsible if there is no vote in the House.

“Representative Klarides should commit to not obstructing a responsible short-term solution as we work towards a balanced, responsible biennial budget and she should actively work to garner some support in her caucus for this mini-budget,” Donnelly said. “Both House leaders should put the people of Connecticut first and work together in a bipartisan fashion.”

The annual session of the General Assembly ended June 7, forcing a special session on the budget. Under the rules of a special session, the House speaker and Senate President Pro Tem Martin Looney, D-New Haven, have control over what is debated: Every bill in the special session is considered an emergency, requiring their signatures to come to a vote.

“I am prepared to sign an emergency-certified bill today calling the Senate into session on Thursday, June 29 to vote on the proposed ‘mini budget’ for the first quarter of the fiscal year,” Looney wrote in a statement earlier this week. “No one wants the governor to run the state by executive order. I am disappointed by these developments and hope that the Speaker reconsiders his position.”

That statement helped cast Aresimowicz as the obstacle.

“I don’t mind taking the heat,” said Aresimowicz, who coaches high school football. “I’m a football coach. The players win the games, and the coaches lose the game, and I’m OK with that.”