Updated 5:18 p.m. | William P. Barr is on track to be confirmed as the next attorney general next week.

Senate Majority Leader Mitch McConnell moved to limit debate and cut off any filibuster threats against the Barr nomination Thursday, setting up votes as soon as the Senate finishes work on a bipartisan package of public lands bills.

The vote to limit debate on the lands bill is scheduled for Monday evening, meaning Barr’s final confirmation should come no later than Thursday.

The Senate Judiciary Committee advanced the Barr nomination earlier Thursday, as Republicans touted his qualifications and Democrats voiced concerns about how he would handle the special counsel investigation.

The 12-10, party-line committee vote sends the nomination to the full Senate. Majority Leader Mitch McConnell, R-Ky., who sets the floor schedule, tweeted Thursday that Barr “has the experience and is eminently qualified” and he expects he will be confirmed next week.

Barr appears to have enough support from Republicans, which have a 53-47 advantage in the chamber, to run the Justice Department. He would replace acting Attorney General Matthew Whitaker as the nation’s top law enforcement official, who has been in the spot since Jeff Sessions was forced to resign in November.

Chairman Lindsey Graham, R-S.C., said before the vote that he begged Barr to get back into public service because he has the kind of experience the country needs at this time. “I think we need a steady hand at the Department of Justice, and I believe he has that steady hand,” Graham said.

Watch: Barr and Mueller are friends? Hearing unlikely to derail attorney general confirmation

Barr, who ran the Justice Department from 1991 to 1993 during the George Bush administration, answered questions during his confirmation hearing last month that indicated he would bring a conservative approach to immigration, law enforcement and civil rights enforcement.

Barr also gave senators key assurances that he would allow Special Counsel Robert S. Mueller III to finish a probe into the 2016 elections and make public as much of the final report as possible. He told them he would resign rather than fire Mueller without cause or change regulations so that could happen.

“I think we all have seen presidents, both Democrats and Republicans, appoint people who are in our judgment political hacks,” Sen. John Kennedy, R-La., said before the vote. “I do not think that any fair-minded person could call Bill Barr a political hack. I just don’t.”

But Democrats said Thursday that Barr’s comments did not go far enough to reassure them.

In part, they say Barr left open possible loopholes in his commitment to airing Mueller’s findings and a broad view of presidential power that might allow Trump to interfere in Mueller and other investigations into his campaign, family or associates.

“I hope I’m wrong. I hope if he’s the next attorney general, and he’s likely to be, that what I saw in his family, what I saw in his resume, what I’ve seen in his commitment to the issue of justice, will come through clearly,” Sen. Richard J. Durbin, D-Ill., said. “And he will stand up for this Constitution, even if it’s against the wishes of this president.”

Among other concerns: Barr would not commit to follow the guidance of career ethics officials on whether he should recuse himself from oversight of the Mueller investigation or commit to defer to Mueller’s investigative decisions. “In essence, Mr. Barr is asking the American people to trust him to do the right thing,” Sen. Chris Coons, D-Del., said in a written statement ahead of the vote.

Sen. Dianne Feinstein of California, the committee’s top Democrat, said that Barr did not commit to providing Mueller’s report to Congress, only follow department rules and regulations on what should be public.

“Nothing in existing law or regulation prevents the attorney general from sharing the report,” Feinstein said before the vote.

Democrats also expressed concern about Barr’s memo he sent to the Justice Department last year, unsolicited, that detailed presidential power and said Mueller had a “fatally misconceived” theory that Trump committed a crime when he fired a political appointee, FBI Director James B. Comey, because that was in his powers as president.

“This is not the time to install an attorney general who has repeatedly espoused a view of unfettered executive power,” Sen. Amy Klobuchar, D-Minn., said.

The committee also advanced dozens of nominations for federal appeals courts and district courts, many on a 12-10, party-line vote. The picks were renominated after their nominations expired at the end of last Congress and must restart the confirmation process.