The law, passed over Hogan's veto last year, requires officials to study local transportation projects, rank them and offer an explanation if any project receives state funding over one that is ranked higher.
Hogan argues the law forces him to eliminate state funding for almost every project in Maryland and could mire projects in litigation. General Assembly Democrats and the Maryland attorney general's office disagree, saying the scoring system is only advisory.
The new legislation, which has the backing of Senate President Thomas V. Mike Miller, amends a bill proposed by Hogan to repeal the scoring law. It would create a panel of legislators and administration officials that would study the new scoring system for two years.
In the meantime, Hogan would be allowed to assign transportation funding under the old rules, which did not require the governor to create a scoring system or explain why he chose to fund one project over another.
If the panel can't agree to changes to the law after two years, the provisions of the law passed last year would go into effect.
The law has been at the center of a political fight between Hogan and Democrats in the General Assembly, but Miller signaled early in this year's session that he'd be open to reaching a compromise.
The amended bill would push any further decisions on the law until after the next gubernatorial election.
Sen. Richard Madaleno — vice chairman of the Budget and Taxation Committee, which passed the new legislation — said it is important for taxpayers to have some insight into the way road and transit projects are selected for funding, but he agreed to the compromise to end the battle with Hogan.
"We're handing him an olive branch and we're hoping he takes it," the Montgomery County Democrat said.
A spokesman for Hogan did not respond to questions about the amended legislation.
A version of the repeal bill also has been introduced in the House of Delegates. It has had a committee hearing but has yet to move forward.