HARTFORD, Conn. — Connecticut lawmakers have some unfinished business to clear up before the new legislative session begins next month.

The General Assembly is scheduled to hold a veto session on Wednesday to override Gov. Dannel P. Malloy’s rejection of a popular, bipartisan bill that restored $54 million to a program that helps about 113,000 seniors and people with disabilities pay for Medicare-related costs.

The scheduled vote comes shortly before the regular legislative session opens Feb. 7. That’s when Malloy will deliver his final State of the State address to a joint session of the General Assembly. The Democrat is not seeking a third term in November.

“The General Assembly has spoken clearly in overwhelmingly voting for the bipartisan plan to restore the Medicare Savings Program,” said Democratic Senate President Martin Looney, of New Haven, shortly after Malloy’s veto. “I expect that Democrats and Republicans will remain consistent in their votes when we are called back for a veto session.”

Malloy had urged lawmakers not to pass the legislation in a special session this month, telling them he had already delayed the cuts until July 1 to give them more time to “explore sustainable changes to the program” while ensuring that benefits would not be interrupted this fiscal year. But lawmakers pressed ahead with a vote Monday, arguing they needed to assure recipients the funding would be restored.

Malloy has argued the budget changes lawmakers made to fund the program “are wishful thinking, double-counting and pushing problems off into the future.” Democrats and Republicans disagree with Malloy’s characterization.

The anticipated veto override could strain relations between lawmakers and the governor, who still have state budget deficit problems they need to solve this year.

House Minority Leader Themis Klarides, R-Derby, said this year “promises to be an interesting year in Hartford.”