Alejandro Mayorkas, President Obama's nominee to become deputy secretary of the Homeland Security Department, testifies July 25 on Capitol Hill. (J. Scott Applewhite/AP)

Two Republican senators ratcheted up their objections Tuesday to the Obama administration’s nominee for the No. 2 job at the Department of Homeland Security, saying he should not be confirmed because of an ongoing internal probe.

The nominee, Alejandro ­Mayorkas, is expected to be approved Wednesday on a party-­line vote in the Senate Homeland Security and Governmental Affairs Committee. His name would then go to the Senate floor, and he could be one of the first Cabinet nominees considered under new Senate rules that permit confirmation with a majority vote.

But in a letter to Sen. Thomas R. Carper (D-Del.), the committee chairman, Republican Sens. John McCain (Ariz.) and Tom Coburn (Okla.) said their “objections remain” to Mayorkas’s confirmation because of an ongoing inquiry by the Department of Homeland Security’s inspector general.

The investigation focuses on allegations that Mayorkas mismanaged the operation of a visa program for wealthy foreign investors. He denies the charges.

The program, known as EB-5, is intended to help create jobs by granting visas to foreign nationals who invest in the United States.

The program is under constant pressure for speedy consideration of applicants from businesses, including one partly owned by Terry McAuliffe, Virginia’s governor-elect.

Mayorkas has said that he showed no favoritism toward McAuliffe or anyone else and rejected complaints lodged against him by unidentified DHS employees. The inspector general’s office, which has been in turmoil over unrelated issues, has found no wrongdoing.

Mayorkas, a former U.S. attorney for Los Angeles, has strong backing from the White House, several advisers to former president George W. Bush and former homeland security secretary Janet Napolitano, who told The Washington Post last week that she strongly supports his confirmation.

In their letter, McCain and Coburn say Carper has “marginalized the concerns” of committee Republicans about Mayorkas’s nomination.

“If the IG investigation subsequently discovers” problems with Mayorkas’s leadership, the letter said, “it would undermine” the committee’s oversight responsibilities.

Carper responded with his own letter Tuesday, saying that the inspector general “has told both of our staffs that they are still several months away from concluding their work. They have also told us that there is no indication of criminal activity” by Mayorkas or others at DHS.

Carper also said that Democrats have not been granted access to the DHS employees who complained about Mayorkas to Coburn and Sen. Charles E. Grassley (R-Iowa).

“I believe there is an overwhelming need for leadership at DHS and overwhelming case that Director Mayorkas will be an excellent Deputy Secretary and should be promptly confirmed,” Carper wrote.