The Republican chairman of the House Homeland Security Committee on Sunday floated possible names for the newly vacant position of Homeland Security secretary, warning an unacceptable pick could hurt President Obama’s chances of passing immigration reform.

Rep. Michael McCaul, R-Texas, criticized the recently departed secretary, Janet Napolitano, for low morale in federal immigration offices and for her assessment that border security has improved under Obama’s watch. McCaul said the next pick is a “real opportunity to get a real leader in that can work with House Republicans.”

McCaul pushed retired Coast Guard Commandant Thad Allen, New York Police Commissioner Ray Kelly and William Bratton, the former top cop in New York, Los Angeles and Boston.

“I think any of three of those coming in would gain a lot of respect from House Republicans and could help us at a time when we’re trying to push this border security measure out of the House of Representatives,” the Dallas lawmaker told "Fox News Sunday."

Kelly has also been named as a potential nominee by Rep. Peter King, R-N.Y., as well as Sen. Chuck Schumer, D-N.Y. Allen drew bipartisan praise for overseeing the federal responses to Hurricanes Katrina and Rita. And Bratton’s law enforcement background would ease minds among those worried about the increased U.S. presence along the Mexico border as a result of immigration reform. “I would be very willing to talk to them about this,” McCaul said. “It’s ultimately the president’s choice.”