Flanked by Senate President Mike Miller, left, newly inaugurated Maryland Gov. Larry Hogan gives his first State of the State address to lawmakers in Annapolis. (Linda Davidson/The Washington Post)

Maryland Senate President Thomas V. Mike Miller Jr. ­(D-Calvert) pledged Wednesday to work with Gov. Larry Hogan (R) on some of Hogan’s struggling tax-relief proposals, including forging a compromise that would shrink a planned increase in the state’s gas tax.

Hogan had proposed eliminating the automatic gas tax increase altogether as a way of delivering on his campaign promise to reduce people’s taxes. But the idea was met with derision by Democratic legislative leaders, including Miller, who said last month that complete elimination of the increase would have no chance of passage in the General Assembly.

On Wednesday, Miller said that Hogan has worked collaboratively with the General Assembly during the ongoing budget negotiations. The Senate gave preliminary, unanimous approval on Wednesday to a budget that would restore funding increases for school systems and pay raises for state workers, both of which Hogan had proposed cutting; reduce the state’s contribution to the employee pension fund by half; and cut the state’s structural deficit by 75 percent.

In the spirit of bipartisanship, Miller said, he wants to see some of Hogan’s agenda considered and possibly advanced.

“I’m just asking the General Assembly to continue to work with the administration so the House can declare victory, the Senate can declare victory and, closing the session, the governor can say to the people who voted for him that he can declare victory as well,” Miller said.

The Senate president offered no details on his proposal to slow the planned increases in the gas tax. He described it as a “downsizing,” where the tax would “only be possibly increased by a small amount each year.”

A 2013 law championed by Hogan’s predecessor, Gov. Martin O’Malley (D), phases in a 5 percent sales tax on gasoline over three years and includes a provision that increases the existing gas tax each year based on the rate of inflation. By mid-2017, legislative analysts say, the increases would cost the typical driver more than $80 a year.

Hogan submitted legislation shortly after taking office that would undo key parts of that gas-tax law, gutting funding for transportation projects in the process.

In addition to looking at the gas tax, Miller said the Senate is also working to move a version of Hogan’s bill to expand charter schools, along with another proposal that would give a minor tax break to small businesses.

The Senate and House have convened work groups to consider amendments to Hogan’s charter bill, which is strongly opposed by the teachers union and local school boards. Key provisions in Hogan’s bill will likely be taken out, senators have said.

The tax cut to small businesses involves the elimination of the personal property income tax for businesses that have less than $10,000 in personal property. Businesses in Maryland currently pay taxes on office furniture, fixtures and equipment.

“Delivering tax relief to the people of Maryland is a major priority for Governor Hogan, and it is great to hear that Senate President Miller is working to achieve the same goals,” said Hogan spokesman Doug Mayer. “We look forward to working with both the Senate and House in the coming weeks to end this session with something Annapolis hasn’t done in a long time — no tax hikes.”

To become law, any compromise forged in the Senate would also have to be approved by the House.

Alexandra M. Hughes, the deputy chief of staff for House Speaker Michael E. Busch (D-Anne Arundel), said Busch would need more information on Miller’s proposal in order to comment.

Busch, like Miller, was strongly opposed to Hogan’s bill eliminating the gas-tax increase, which according to a report issued last month would cost the state $3 billion in funding for planned road and transit projects over the coming six years.

There are no estimates on how much a “downsize” would cost.

Another Hogan tax proposal — one that would give a tax break to corporations that donate to private and public schools — appeared on Wednesday to be stalled in the House.

Del. Sheila E. Hixson (D-Montgomery), chairman of the House Ways and Means Committee, said the bill remains in her committee and will “probably not” move this year.

Hixson said her committee heard testimony for seven of Hogan’s nine bills. Some of the proposals “have costs attached to them,” she said. “We’re not doing taxes. . . . Now that the budget is balanced, they don’t want us to offset anything.”

The Senate is scheduled to consider the budget and a companion bill that balances the budget on Thursday for a final vote. It has approved 44 amendments to the House budget bill.

Senators added $24 million to the budget, including $15 million for Dimensions Hospital Center in Prince George’s County and $5 million in additional Medicaid rate reimbursements.

The longest discussion on the bill was over the Senate’s proposal to give the owners of cranes in the Port of Baltimore a tax exemption on the cranes. Sen. James E. DeGrange Sr. (D-Anne Arundel) said Baltimore and Baltimore County, not the state, would lose revenue from the exemption.