JUNEAU — Gov. Bill Walker said Monday that he would like legislators to continue their work in Juneau, even if that means relocating from the Capitol while it undergoes renovation work.

The Alaska Legislature went into overtime Monday with no resolution on dealing with an estimated $4 billion state budget deficit. Senate President Kevin Meyer, R-Anchorage, said that by Wednesday lawmakers should be able to tell if their work can be completed within a few days.

Renovation work on the Capitol began Monday, and the construction schedule aims to have the Capitol effectively cleared out by May 2. By Saturday, though, “we’re not going to be welcome in this building anymore,” Senate Majority Leader Coghill said, adding that it will become noisier.

Walker said he would like to see legislators finish their work in Juneau. Unless legislators live in Juneau, they are there for one reason — to do the state’s business, he said. He also noted the significance of having the public affairs channel based in Juneau broadcasting legislative goings-on.

Lawmakers worked past the voter-approved 90-day session limit on Sunday and cleared a backlog of bills during marathon floor sessions that ended early Monday. They now want to limit their focus to budget- and revenue-related bills as they try to reach a compromise to end the session. Items on the list include oil and gas tax credits, tax bills, proposals to allow for structured annual draws from Alaska Permanent Fund earnings, a proposed criminal justice system overhaul and state budgets.

A bill was introduced in the House Monday seeking to suspend merit pay increases for state employees.

Alaska’s Constitution allows for regular sessions of up to 121 days with an option to add another 10.

Tax credits have been a major stumbling block, particularly in the House. A resolution on that issue is seen as key to making further progress on the budget and revenue bills.

Coghill, R-North Pole, said he expects that two bills that faltered on the House and Senate floors will have to wait until next year. “On these particular issues, the conference committee would have been more complex than time would allow,” he said.

The House rejected Senate changes to a parental rights and student testing bill that limited who could teach sex education in schools. The Senate rejected a House change to an alcohol-related bill adding provisions related to the Board of Barbers and Hairdressers.

The alcohol bill included provisions sought by marijuana regulators to allow for national criminal history checks for applicants who want to open legal pot businesses. The background-check provisions are in another bill that negotiators have struggled to reach an agreement on.

Rep. Wes Keller, who sponsored the parental rights and student testing bill, said the sex education language made the bill contentious. He said it’s possible the House could take up the vote again but called that a “slim thread.”

Walker wants lawmakers to approve a fiscal plan to help dig the state out of a deficit exacerbated by low oil prices. He has said he considers reduced spending, restructuring of permanent fund earnings and the dividend program and new revenues that include a broad-based tax as key elements for a sustainable budget.

If pieces of his plan are scuttled, he wants something in their place with a similar fiscal impact. Walker said he was concerned about a legislative draft that would delay implementation of a proposed state income tax until 2019, two years later than he proposed.

The Senate passed a resolution last month urging that any special session that might be called be held in a community on the road system. Juneau isn’t on the system.