John Roth, President Obama’s nominee for inspector general of the Homeland Security Department, talks to a Senate panel on Wednesday. (Pablo Martinez Monsivais/ASSOCIATED PRESS)

A Senate panel on Wednesday signaled strong bipartisan support for John Roth, President Obama’s nominee for Department of Homeland Security inspector general, and focused on key issues they want him to monitor if he gets confirmed.

Members of the Senate Homeland Security and Governmental Affairs Committee said they are hoping for a swift confirmation, but a date has yet to be set for a vote that would send Roth’s nomination to the full Senate.

Roth, who has led the Food and Drug Administration’s criminal investigations division since last year, would take charge of an office recovering from turmoil after former acting head Charles K. Edwards stepped down last month. The Senate had been investigating allegations that Edwards engaged in nepotism and covered up details of the Secret Service’s Colombia prostitution scandal.

Edwards, who now works for Homeland Security’s science and technology division, called the claims “false allegations” and “personal attacks” in a statement last year.

Sen. Claire McCaskill (D-Mo.), a member of the Homeland Security panel, said she expects management challenges because of the controversy.

“You’ve got a staff divided between those who were making the accusations against Mr. Edwards and those who were hired and remain loyal to Mr. Edwards,” she warned Roth.

Roth said: “One of the things that I’ve found in agencies that have morale problems and have these kind of warring camps is a lack of focus on mission. I think it’s very important to refocus people on the very important mission that the inspector general’s office has.”

If confirmed, Roth would take over an investigation into whistleblower claims against Alejandro Mayorkas, the former U.S. immigration director and new No. 2 at Homeland Security, who allegedly helped secure foreign-worker visas for a firm tied to Virginia Gov.-elect Terry McAuliffe (D) and Anthony Rodham, a brother of Hillary Rodham Clinton.

Mayorkas, who was confirmed for his post last month with a party-line vote, has denied the claims. During a July hearing, he acknowledged meeting with McAuliffe but said he only talked with him generally about the application-review process.

Sen. Tom Coburn (Okla.), the ranking Republican of the committee, opposed Mayorkas’s confirmation because of the probe. He insisted Wednesday that a new inspector general should prioritize the investigation.

“It’s important that it be completed, that it be accurate for the benefit of Mr. Mayorkas, that it is completed in a prompt manner and in a way that nobody can attest or challenge its scholarly basis,” Coburn said.

Lawmakers said they also want to see continued reviews of the Secret Service’s prostitution scandal and alleged abuses of overtime pay at Customs and Border Protection.

An inspector general’s report last month said sexual misconduct is not widespread within the Secret Service, but Sen. Ronald H. Johnson (R-Wis.) questioned whether the analysis, conducted while Edwards was in charge, was vigorous enough. Roth said he did not want to comment on the findings without talking to the report’s authors.

The allegations of overtime abuses came from an Office of Special Counsel report that found a “profound and entrenched problem” with Customs and Border Protection desk employees misusing a form of overtime intended for field agents who work unanticipated extra hours while fulfilling their law-enforcement duties.

“My sense is that it’s a statutory problem that probably lends itself to a statutory fix, but this is something I’d certainly be happy to take a look at if I’m confirmed,” Roth said.

Before joining the FDA, Roth worked as a prosecutor and manager at the Justice Department for 25 years and served on the 9/11 Commission.

Obama has struggled to fill many of the key positions at Homeland Security, which is the third-largest executive department and home to agencies such as Customs and Border Protection, the Coast Guard, the Transportation Security Administration and the Federal Emergency Management Agency. About 40 percent of the top positions within the department are unfilled or held by acting officials.

In recent months, Obama has made progress in choosing nominees for some of the leadership openings, and new Senate rules will prevent Republicans from filibustering to block votes on those picks, as they did at a record pace during Obama’s first term.

With the new guidelines in place, the Senate last month confirmed Jeh Johnson, former general counsel for the Pentagon, to serve as secretary of homeland security.

Homeland Security’s senior-leadership scores ranked last among large agencies in 2013’s “The Best Places to Work in the Federal Government” report, which is based on the government’s annual employee-viewpoints survey. The department earned 35 points out of 100.