House Homeland Security Committee Chairman Rep. Mike McCaul, R-Texas is under consideration for DHS secretary. (AP Photo/J. Scott Applewhite, File)

President-elect Donald Trump is considering two Republican members of Congress forDepartment of Homeland Security secretary, a critical post whose occupant would oversee his proposed crackdown on illegal immigration, people familiar with the deliberations said.

The incoming chief executive is looking at Rep. Michael McCaul (R-Texas), chairman of the House Homeland Security Committee, and Sen. Jeff Sessions (R-Ala.), the people said. Sessions, who helped shape Trump’s hardline views on immigration, is also under consideration for other top administration jobs such as defense secretary.

Other names being floated for the Homeland Security post include former New York City mayor Rudy Giuliani and New Jersey Gov. Chris Christie, who leads Trump’s transition team. But both are former U.S. attorneys also reportedly interested in being attorney general, so they could view DHS as a consolation prize.

Several government officials said they had been told that a more incendiary choice – ousted Arizona sheriff Joe Arpaio – is also under consideration. Arpaio, a vocal Trump supporter who lost his re-election bid this week, is known for forcing inmates to wear pink underwear and has long been accused of anti-Hispanic bias.

But other people familiar with the deliberations said Arpaio is viewed as unable to win Senate confirmation. He is also 84-years-old and facing legal trouble. The longtime sheriff was recently charged with criminal contempt for resisting a judge’s order that he stop detaining people solely on suspicion they were undocumented immigrants. Arpaio, whose wife is battling cancer, could face up to six months in jail if convicted.

Few jobs are likely to be higher profile in the Trump administration than chief of DHS, the third-largest Cabinet department with more than 240,000 employees who do everything from fighting terrorism to protecting the president and enforcing the nation’s immigration laws. Trump has pledged a crackdown on illegal immigration that would be unprecedented in American history and would require an exorbitantly expensive – and logistically difficult – operation to remove millions from the country.

Overseeing it all would be DHS, which was created after the Sept. 11, 2001 attacks primarily to coordinate the battle against terrorism but is now perhaps equally known for its immigration role. A beefed-up U.S. Immigration and Customs Enforcement (ICE), a DHS component, will be instrumental if Trump follows through on rounding up far more undocumented immigrants. U.S. Customs and Border Protection, also part of DHS, would come under increased pressure to better secure the southwest border.

Perhaps the DHS’s secretary’s most controversial role would be to help oversee the building of Trump’s wall along that border. The wall is the president-elect’s signature proposal, but experts say it would face numerous obstacles, such as environmental and engineering problems and fights with ranchers and others who would resist giving up their land.

The candidates would bring different strengths to the secretary position, a job made even more challenging by DHS’s persistent management problems and employee morale that is among the federal government’s lowest.

McCaul is considered among the few leading Republicans with homeland security experience likely to be called upon for advice by Trump, since the previous GOP homeland security secretaries – Tom Ridge and Michael Chertoff – blasted the GOP candidate in highly personal terms during the campaign.

“Anyone closely associated with the two of them is likely to be suspect at best and persona non grata at worst,’’ said a former homeland security official, who spoke on condition of anonymity to candidly discuss the leading candidates.

Sessions would bring familiarity with immigration and strong views on the subject, while Giuliani and Christie would bring management skills and close personal relationships with Trump.

Easily the most controversial choice would be Arpaio, long known for his tough immigration enforcement. The sheriff of Arizona’s Maricopa County, he was defeated Tuesday in his bid for a seventh term by his Democratic challenger.

Word that Arpaio might be under consideration for DHS drew consternation Thursday in law enforcement circles, where he is considered by some to be a highly political maverick. Yet selecting Arpaio could win Trump plaudits from his political base.

“If Trump is really embracing the seriousness of being President,’’ one former homeland security official said, “I hope he would see the complexities of DHS and not try to compare that to running a sheriff’s office.’’