Deputy Labor Secretary Julie Su prepares to testify before the Senate Health, Education, Labor and Pensions Committee during her confirmation hearing to be the next secretary of the Labor Department in the Dirksen Senate Office Building on Capitol Hill on April 20 in Washington, DC.
CNN  — 

A Senate committee voted along party lines on Wednesday to move forward with President Joe Biden’s pick to lead the Department of Labor, marking a key milestone in the nomination process amid high-level efforts by the White House to secure Julie Su’s confirmation.

Democrats on the Senate Health, Education, Labor, and Pensions Committee all voted in support of Su. She did not receive the support of any Republicans.

The nomination will next be considered by the full Senate. But it’s not clear yet whether Su, currently the acting secretary of labor, has secured the votes of key Senate Democrats. Without their support, the nomination would likely fail.

An administration official told CNN that the White House has been engaging in a number of high-level efforts to galvanize support for Su. That includes holding nightly war room calls to track real-time updates and 15-20 external check-in calls per day across labor and business groups.

Along with assembling together a diverse slate of supporters – which includes a long list of major union groups, stakeholder groups and lawmakers – the White House has also enlisted Marty Walsh, who left his role as Biden’s labor secretary earlier this year, to help get Su’s confirmation across the finish line.

Walsh is actively working with groups and senators to confirm Su, the official said.

Despite a narrow majority in the Senate, Democrats have with more recent frequency failed to sign off on high-profile Biden appointees. And if Su does not secure enough support from the Senate, she would be the highest-ranking Biden nominee so far to fail to be confirmed.

A failed nomination would leave a Cabinet-level vacancy for a jobs-focused role at a critical time – as Biden works to secure a second term in office and as the nation continues to grapple with the possibility of a recession.

Su was narrowly confirmed to be the deputy secretary of labor in 2021, receiving unanimous support at the time from Senate Democrats and no support from Republicans. And this time around, she’s also largely expected to have no support from Senate Republicans.

Su’s Republican critics in the Senate have argued that her policy stances are hostile to small businesses. She has also faced scrutiny for California’s handling of unemployment benefits during the Covid-19 pandemic – particularly her oversight of the state’s Employment Development Department.

A lack of Republican support would mean that in the 51-49 Democratic-controlled Senate, more than two defections from the Democratic caucus could tank the nomination. And if California Sen. Dianne Feinstein, who has been away from Congress while recovering from shingles for the past two months, or another Democratic senator is absent, the path would narrow ever more.

Two Democratic senators up for reelection in red states, Montana Sen. Jon Tester and West Virginia Sen. Joe Manchin, are not yet ready to throw their support behind her. It’s also not clear how Arizona independent Sen. Kyrsten Sinema, who left the Democratic Party last year but kept her committee assignments with the majority, will vote.

Su has met with Tester, the administration official confirmed. Sinema has also spoken with Su to discuss the nomination, her office told CNN.

Tester told reporters on Wednesday that he is still considering whether to support Su following their meeting.

“We had a good conversation. I told her what I was concerned about. She responded appropriately. I just want to think about it some more,” Tester said.

The narrow majority in the Senate has proven to be a challenge for other Biden nominees in recent months, with Democrats failing to sign off on Phil Washington’s nomination to lead the Federal Aviation Administration as well as Gigi Sohn’s nomination to the Federal Communications Commission.

Biden is continuing to stand by his labor nominee, telling union workers on on Tuesday – just hours after his reelection bid was announced – that Su is “gonna be a great secretary.”

This story and headline have been updated with additional developments.

CNN’s Nikki Robertson contributed to this report.