President Obama said early Thursday that he wants to make a major push to have Congress pass immigration legislation this year — but by late in the day the White House was confirming he will nominate someone with little immigration experience to head the Department of Homeland Security.

Administration and congressional officials said Mr. Obama will turn to Jeh Johnson, who was the top lawyer at the Pentagon, to run the agency that oversees the Secret Service, the Transportation Security Administration, the Federal Emergency Management Agency and all three immigration services.

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“The president is selecting Johnson because he is one the most highly qualified and respected national security leaders, having served as the senior lawyer for the largest government agency in the world,” a White House aide said.

A nomination could come Friday for the job, which many observers say is the toughest in Washington, getting battered from all sides on issues of privacy and security, and on how strenuously the department is enforcing immigration laws.

With the end of the government shutdown, Mr. Obama has elevated immigration to the top of his legislative agenda, saying Thursday that he will pressure House Republicans to pass a bill, following the lead of the Senate which passed one in June.

“This can and should get done by the end of this year,” he said, adding that he expected it to be an area of cooperation with the GOP.

Some key Republicans, though, said judging by the way the president refused to negotiate with them during the spending and debt fights, he’s squandered any chance to work with them now.

“I think it would be crazy for the House Republican leadership to enter into negotiations with him on immigration, and I’m a proponent of immigration reform,” Rep. Raul R. Labrador, Idaho Republican, said Wednesday. “He’s trying to destroy the Republican Party, and I think that anything that we do right now with the president on immigration will be with that same goal in mind, which is to destroy the Republican Party and not to get good policy.”

Where the Senate passed a broad bill combining more spending on border security with a revamp of the legal immigration system and a legalization program for those in the country illegally, House Republican leaders have said they will tackle the issue in pieces.

Speaking alongside Mr. Labrador at the Heritage Foundation on Wednesday, Rep. Matt Salmon, Arizona Republican, said he had been promised by House Speaker John A. Boehner that the House will not go to conference committee to work out differences with the Senate on a big bill, only on the small pieces.

A spokesman for Mr. Boehner said the speaker was reiterating “his long-standing support for a step-by-step process to fix our broken immigration system.”

Key to the House GOP’s efforts will be a bill to legalize younger illegal immigrants, known as Dreamers. House Majority Leader Eric Cantor of Virginia is trying to write that bill along with Rep. Bob Goodlatte, Virginia Republican and chairman of the Judiciary Committee.

Mr. Johnson’s nomination will help renew the immigration debate — though his experience with the issue seems limited.

“There doesn’t seem to be any indication that he has any experience at all in immigration,” said Rosemary Jenks, chief lobbyist for NumbersUSA, which advocates for stricter immigration limits.

Indeed, reaction from either side of the immigration debate was muted as everyone tried to figure out what to make of Mr. Johnson.