Republican legislative leaders took Democratic Gov. Dannel P. Malloy seriously when he told them to jot some budget cutting ideas on the back of an envelope and he would take a look at them.

They met him halfway. Senate Republican Leader Len Fasano and House Republican Leader Themis Klarides didn’t offer any specifics for cuts in writing, but they did send their request to meet with Malloy Thursday on the back of an envelope.

“We have several ideas on how to eliminate the deficit,” the two wrote. “We would love to have a meeting with you and our Democratic colleagues to discuss them.”

Malloy responded by sending out a Tweet on the front on an envelope to let the two know he was going to have lunch in the Legislative Office Building cafeteria at “noon” and they should bring their ideas “in writing if possible. I’ll have someone hold a table.”

Klarides tweeted back “It’s a date!”

The back and forth between Republican lawmakers and Malloy caps a week of partisan fighting over a new $121 million budget deficit revealed Tuesday evening.

Malloy believes he’s capable of handling the budget deficit, which is less than 1 percent of the total $20 billion, without the legislature’s help. He has the statutory authority to cut up to 5 percent of any line item in the budget. The last time legislative Republicans were invited to participate in budget talks was in December 2012 when the budget deficit reached the 1 percent threshold and required legislative approval.

It might not be there yet. However, if the Republicans’ math is correct the state may already have reached that 1 percent threshold.

In a letter to Senate President Martin Looney and House Speaker Brendan Sharkey, which accompanied the envelop, Republicans said the calculation of the $121 million deficit “assumes that the state can count on an additional $45 million in random, unidentified tax initiatives — and questions remain as to whether this will actually be collected.”

When the legislature adopted the budget back in May it assumed the Department of Revenue Services would collect an additional $75 million in back taxes. As of December, the department reported that it had collected only about $30 million.

Republicans also believe the governor’s budget office estimate “fails to recognize a $35 million hole in retiree healthcare needs identified by the comptroller as well as a $7 million deficiency in the Department of Correction budget.”

Malloy’s budget office referred all questions regarding the issue to the governor’s press office, which sent out the tweet regarding Friday’s meeting at noon.

Republican lawmakers have maintained that no single party, as Malloy said in his inaugural address, holds the monopoly on good ideas.