The Maryland Senate approved legislation Tuesday that would provide another source of retroactive health insurance for Marylanders who tried to get coverage through the state’s troubled insurance marketplace, encountered problems and were left uncovered through no fault of their own.

The legislation now moves to the House of Delegates.

The bill would expand enrollment in the Maryland Health Insurance Plan, a state program that is more than a decade old and covers high-risk individuals. To qualify, residents would have to prove they unsuccessfully attempted to obtain insurance through the new Maryland Health Benefit Exchange. They could opt to have the insurance retroactive to Jan. 1, and enrollment would close March 31.

This insurance is considered temporary and a last resort. Enrollees would pay a premium, which is determined by income but is often higher than market rates. The temporary coverage would be terminated as soon as permanent insurance became available through the exchange.

State officials originally expected anywhere from a few hundred to 5,000 people to sign up for the insurance, which could have cost as much as $10 million. Last week, the four insurance carriers participating in the Maryland health exchange agreed to offer insurance retroactive to Jan. 1, as long as people signed up by Tuesday at 5 p.m. and paid their first two months of premiums. As of Monday, 599 households had registered for the retroactive insurance, according to an exchange spokeswoman. Although the deadline to register was Tuesday at 5 p.m., the exchange will continue to process these enrollments in the coming days. With that option available, state officials expect that only a few hundred will need temporary, retroactive insurance through the state.

“There have been glitches, there may continue to be glitches,” said Sen. Thomas M. Middleton (D-Charles), the chairman of the finance committee, which handled the bill. “This is just a safety net. How many people it’s going to cover? I don’t know. But to me, I want to have this satisfaction. . . . I’m sure there’s going to be someone that’s going to fall through the cracks.”

The emergency legislation was approved by a 38 to 8 vote Tuesday morning. All eight dissenting votes came from Republicans. Just before the vote, Senate Minority Leader David R. Brinkley (R-Frederick) urged his colleagues to vote yes.

“I don’t think that the whole Obamacare or the state health exchange or anything that you want to call it is the way that the state should have gone and should be the law of the land — but it is. And because it is, these people were harmed, and this is certainly a short-term remedy for that,” Brinkley said. “This is the public statement that the state messed up.”

Senators debated the bill for nearly an hour Monday night, with a handful of Republicans asking questions.

They asked some about the legislation, such as how the state would determine who was eligible for the temporary assistance. But most focused on the troubled exchange.

Several senators said they were frustrated by the lack of information they received about the exchange’s problems. They wanted to know why the committee is not fully investigating what caused the disastrous launch of the site before approving legislation to allow health officials to spend more money.

“The reason why we have this piece of legislation before us is because of this gross mismanagement that occurred,” said Sen. Christopher B. Shank (R-Washington).

Middleton said the committee is in the process of investigating what happened and has requested a number of documents related to the exchange. Middleton has previously said that although there were many missteps in the creation of the site, he does not believe anything illegal occurred. He added that everyone is anxious to see the exchange fully operational.

Senate President Thomas V. Mike Miller Jr. (D-Calvert) told reporters Tuesday that he wants a “full explanation” of what happened, especially for how contractors were selected.

“I’m not looking to blame anyone,” he said. “I’m just looking for explanations.”

On Monday night, a few of the senators questioned the security of sensitive information obtained by the exchange, especially following news this weekend that the exchange mailed out Medicaid enrollment packages that contained the wrong names.

Middleton defended the security of the site and said some of the exchange’s problems can be blamed on the intense need for security.

“Maryland wanted to devise the safest system as it can, and any time you have a safe system, that means that it’s going to be harder to get into,” Middleton said. “That, in its essence, may be part of the problem, why it’s so hard to get the system up and going.”

A bulk of the questioning came from Sen. Edward R. Reilly (R-Anne Arundel), who stood on the floor for nearly 30 minutes Monday and voted for the legislation Tuesday. Reilly wrapped up by saying that he’s “very concerned” about the flawed system and listed off problems his constituents have had.

“This is a problematic situation,” he said. “And I hope that the committee tries to get some answers and fill in the blanks.”

To that, Miller told him: “I would suggest: You’re a senator. You address the situation. I mean, that’s what I hope each one of these 47 senators does when they get these questions. . . . That’s what we’re here for.”

On Tuesday morning, Reilly responded to Miller: “We did work with them, Mr. President. . . . Be assured that we are trying our very, very best to work with our constituents that have problems. It’s difficult out there.”