The fate of a bill to give in-state tuition breaks to undocumented immigrants hung in the balance Monday as Senate lawmakers refused to sign off on House-backed changes to the measure.

With the legislative session concluding at midnight Monday, it was uncertain whether supporters could revive the bill that would allow illegal immigrants who have graduated from Maryland high schools to pay in-state tuition at the state’s colleges.

Sen. Joan Carter Conway (D-Baltimore) said the Senate’s action had effectively killed the bill.

After a series of narrowly decided votes, Senate lawmakers sent the bill to conference committee because of fresh concerns that it would not do enough to ensure that the parents or guardians of the undocumented students are Maryland taxpayers. Republican lawmakers, and some Democrats, said the House-backed changes permitted a sizeable loophole to the tax requirement.

“Let’s be clear,” said Senate President Thomas V. Mike Miller Jr. (D-Calvert). “It’s not the minority party that is killing this bill. It’s Democrats … who are no longer comfortable with the bill.”

When it became clear that Democrats could not round up the required 29 votes to cut off a Republican-led filibuster, legislators moved to confer with House lawmakers to try to work out the differences between the two chambers.

Senate Majority Leader Robert Garagiola (D-Montgomery) said he thought legislators could move quickly to keep the bill alive before the session ends.