President in WSJ CEO Council Interview Also Discusses Immigration, Iran and Health Law

President Barack Obama said Tuesday he would accept a piecemeal approach to overhauling the immigration system, a move aimed at jump-starting a moribund process that reflects the realities of a divided Congress.

Mr. Obama has long favored the sweeping immigration bill that passed the Senate in June, but the House has made clear it wouldn’t consider that measure. In a wide-ranging interview before business executives at The Wall Street Journal CEO Council, the president said he is amenable to House Republicans’ taking up elements of the Senate bill, as long as the end result is the same.

“If they want to chop that thing up into five pieces, as long as all five pieces get done, I don’t care what it looks like,” Mr. Obama said.

But just after Mr. Obama spoke, Rep. Paul Ryan (R., Wis.), chairman of the House Budget Committee, poured cold water on that idea. In his own appearance before The Wall Street Journal CEO Council, Mr. Ryan said there wasn’t enough time left to tackle immigration this year.

Beyond immigration, Mr. Obama also detailed some of the sanctions relief that world powers may give Iran in exchange for Tehran’s halting parts of its nuclear program.

The president is facing criticism over the prospect that the U.S. and its allies would relieve some sanctions without gaining a more robust commitment from the Iranians to curtail their nuclear program. But Mr. Obama said any deal would initially leave the toughest sanctions in place.

“Part of the reason I have confidence that the sanctions don’t fall apart is because we’re not doing anything around the most powerful sanctions: the oil sanctions, the banking sanctions, the financial-services sanctions,” Mr. Obama said. “Those are the ones that have really taken a big chunk out of the Iranian economy.”

On the hottest domestic issue dogging the White House, the president indicated his administration is considering a relaunch of the government’s troubled health-care website, which has frustrated Americans looking to purchase insurance.

He said he was confident the system eventually would succeed. But given the problems plaguing the site, he said, “We’re going to have to, obviously, remarket and rebrand, and that will be challenging in this political environment.” An administration aide said Mr. Obama was referring to the need to persuade Americans to see the law more positively once the website is working properly.

The president’s proposals have stalled in Congress during his second term, among them plans to boost infrastructure spending, expand early-childhood education and raise the federal minimum wage. His approval rating has taken a hit amid the bungled rollout of the health law, which he described as “rough—to say the least.”

“My understanding is, nobody in this town is doing particularly well at the moment when it comes to the opinions of the American people,” Mr. Obama said.

Still, the president said the American economy was “poised for a breakout,” and he sought to befriend an audience that has at times had a tense relationship with the White House, telling the room full of chief executives: “I’m rooting for your success.”

As part of his use of executive power to push his economic agenda, Mr. Obama announced a $100 million high-school grant program aimed at finding new ways to better prepare students for a global high-tech economy.

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