Senate Majority Leader John Thune said he offered Democrats an opportunity to address their biggest priority in an effort to end the government shutdown — but it was not enough to end the stalemate.

Thune, during an interview on MSNBC that aired Thursday morning, said he has offered Democrats a vote on extending the Affordable Care Act premium subsidies, but that he couldn’t guarantee an outcome.

“I’ve told them. I said, and I’ve said, ‘We are willing to have the conversation.’ I’ve said, ‘If you need a vote, we can guarantee you get a vote by a date certain.’ At some point Democrats have to take yes for an answer,” Thune said in the interview, which was taped Wednesday.

Senate Democrats have been demanding fixes to health care to avoid a spike in premiums for many low- and middle-income Americans to unlock their support for funding the government. Democrats have been unwavering in their demands as the shutdown drags on into its 16th day.

The Senate failed on Wednesday for a ninth time to advance the GOP’s government funding bill. On Thursday, the Senate is set to vote again on the short-term government funding bill — but Thune is set to try a new tactic, adding a procedural vote on a bill that would fund the Department of Defense for the full calendar year and ensure paychecks for the troops.

Thursday’s vote is a different sort of vote than previous ones related to the shutdown. This vote begins debate on one of 12 regular order annual appropriations bills that keep the government running.

Thune has signaled that if the Senate does successfully support this package Thursday, he’ll attempt to affix funding bills for additional agencies to it using regular order on the Senate floor.

Reopening the government is a crucial first step to continue discussions about reforms to health care, Thune said on MSNBC. He committed to conversations, but not an outcome. 

“There is a path forward, I believe, but it has to include reforms, and can I guarantee an outcome? No. And that’s what people want to see — guarantee us that this is going to pass,” Thune said. “I can’t guarantee it’s going to pass. I can guarantee you that there will be a process and you will get a vote.” 

Asked about Thune’s comments, Speaker Mike Johnson reiterated Thursday morning that no health care outcomes can be guaranteed.

“It’s not possible for Leader Thune to guarantee to Chuck Schumer some outcome on that, because we haven’t finished those deliberations. I mean, that’s just as simple as it is,” Johnson said during his Thursday morning news conference.

There is bipartisan interest, Thune said, in keeping health care costs down. But changes to the program need to be made, and negotiations on those changes start with opening the government, Thune said. 

Thune was pressed on efforts by the White House to rescind congressionally appropriated funds. Democrats have said that the use of rescissions has made them leery to work on funding deals. Thune did not explicitly say he wanted the White House to stop making rescissions, but he said regular order appropriations were the preferred method.

“The rescission power is something that constitutionally the president has — the question of whether they use it or not — yeah, I mean, that’s obviously something I think that they would need to talk to the White House about,” Thune said.

He said he’s had “conversations” on the topic with the White House and that “I do think that it’s in everybody’s best interest, including the White House’s, to have a normal appropriations process where people are bought in.”

As Thune sat for this interview, the House was in its third consecutive week of recess. Thune was asked if it was the right choice for the House to remain out of town. He said it was a “judgement call” for Speaker Johnson to make. 

“There isn’t anything right now. They did their job. They passed their bill. The game is in the Senate,” Thune said.

He also couldn’t guarantee the shutdown would end any time soon. When asked by Ali Vitali if he thought it would be over by Thanksgiving, Thune didn’t commit. 

“I hope it doesn’t last through Thanksgiving, because that’s going to be a lot of harm to the American people,” he said.

ABC News’ Lauren Peller contributed to this report.