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“I believe we need to focus more of our time and resources on addressing mental health instead of cracking down on law-abiding gun owners and infringing upon our Constitution’s Second Amendment,” Sen. Richard F. Colburn, Dorchester Republican, said last week.

Republicans have struggled to halt Mr. O'Malley’s legislation thus far this session, but his toughest fight could be over transportation, as he has long been unsuccessful in calling for tax increases — particularly in the 23.5-cents-a-gallon gas tax — to fund repairs to the state’s aging infrastructure.

Senate President Thomas V. Mike Miller Jr., Prince George’s Democrat, said last week that he expects the governor to propose a new bill Monday.

Mr. O'Malley met last week with the Senate president and House Speaker Michael E. Busch, Anne Arundel Democrat, to discuss transportation funding, but representatives for the governor have declined to say how close they are to finalizing a bill.

“We’re working toward coming up with a plan that everyone can agree upon that gets us where we need to be,” O'Malley spokeswoman Raquel Guillory said.