WASHINGTON — Defending the shaky rollout of his health care law, President Barack Obama said frustrated Americans “definitely shouldn’t give up” on the problem-plagued program now at the heart of his dispute with Republicans over reopening the federal government.

Obama said public interest far exceeded the government’s expectations, causing technology glitches that thwarted millions of Americans when trying to use government-run health care websites.

“Folks are working around the clock and have been systematically reducing the wait times,” he said.

The federal gateway website was taken down for repairs over the weekend, again hindering people from signing up for insurance.

Obama, in a wide-ranging interview with The Associated Press, also disclosed that U.S. intelligence agencies believe Iran continues to be a year or more away from having the capability to make a nuclear weapon. That assessment is at odds with Israel, which contends Tehran is on a faster course toward a bomb.

He expressed optimism about the blossoming diplomacy between his administration and Iran’s new president, but said the U.S. would not accept a “bad deal” on the Islamic republic’s nuclear program.

The president spoke to the AP on Friday, four days into a partial shutdown of the federal government that has forced 800,000 people off the job, closed national parks and curbed many government services.

Obama reiterated his opposition to negotiating with House Republicans to end the shutdown or raise the nation’s debt ceiling.

“There are enough votes in the House of Representatives to make sure that the government reopens today,” he said. “And I’m pretty willing to bet that there are enough votes in the House of Representatives right now to make sure that the United States doesn’t end up being a deadbeat.”

On other points, Obama:

• Contrasted his tenure as a senator with the current crop of first-term Republican senators, saying he “didn’t go around courting the media” or “trying to shut down the government” while he was in the Senate.

• Said he’s considering keeping some American forces in Afghanistan after the war formally ends in late 2014, if an agreement can be reached with the Afghan government. He tried to do the same in Iraq but was unable to reach an agreement with its government.

• Suggested that the owner of the Washington Redskins football team consider changing its name because, the president said, the current name offends “a sizable group of people.”

With no sign of a breakthrough to end the government shutdown, Obama said he would be willing to negotiate with Republicans on health care, deficit reduction and spending — but only if House Speaker John Boehner, R-Ohio, holds votes to reopen the government and increase the nation’s borrowing limit.

Some House Republicans are seeking health care concessions from Obama in exchange for approving government financing and want more spending cuts before raising the debt ceiling.

The Treasury Department said the nation will hit its borrowing limit around Oct. 17. Obama didn’t specifically rule out taking action on his own if Congress fails to increase the debt ceiling, but said he doesn’t expect to get to that point.

Obama, who successfully ran for president as a first-term senator, also spoke critically about first-term Republican senators, such as Ted Cruz of Texas, who have been leading efforts to shut the government if Republicans can’t extract concessions from the White House.

The president said that when he was in the Senate, he “didn’t go around courting the media. And I certainly didn’t go around trying to shut down the government.”

“I recognize that in today’s media age, being controversial, taking controversial positions, rallying the most extreme parts of your base, whether it’s left or right, is a lot of times the fastest way to get attention and raise money,” he said. “But it’s not good for government.”

The deadline for keeping the government open coincided with the Oct. 1 start of sign-ups for the insurance markets at the center of the health care overhaul Obama signed into law during his first term. Government websites struggled in the first week to keep up with high demand for the new marketplaces. It’s not clear that more than a few managed to enroll the first day.

Obama said he didn’t know how many people had enrolled. Administration officials have said they do not plan to release real-time data on the number of people enrolling, though some states running their own exchange websites are doing so.

The president predicted that when the six-month signup window for the insurance exchanges ends, “we are going to probably exceed what anybody expected in terms of the amount of interest that people had.”

In the flurry of domestic issues consuming his second term, Obama has launched a diplomatic outreach to Iran, aimed at resolving the dispute over Tehran’s nuclear program. Last week, he spoke by phone with President Hassan Rouhani, marking the first direct exchange between U.S. and Iranian leaders in more than 30 years.

“Rouhani has staked his position on the idea that he can improve relations with the rest of the world,” Obama said. “And so far he’s been saying a lot of the right things. And the question now is, can he follow through?”

But Obama said Rouhani is not Iran’s only “decision-maker. He’s not even the ultimate decision-maker,” a reference to the control wielded by Iran’s supreme leader, Ayotollah Ali Khamenei.

Given the supreme leader’s broad influence, some countries, most notably Israel, have questioned whether Rouhani actually represents real change in Iran or just new packaging of old policies.

Obama also put distance between U.S. and Israeli assessments of when Iran might have the capacity to build a nuclear weapon. Israeli officials have said Iran is just months away from being able to build a bomb, while Obama said Tehran was a year or more away.

The president used the same timetable in March, before traveling to Israel. The U.S. and Israel contend that Iran’s nuclear program is aimed at building a bomb, while Tehran says it is enriching uranium for peaceful purposes.

On the 12-year war in Afghanistan, Obama said he would consider keeping some American forces on the ground after the conflict formally ends next year, but acknowledged that doing so would require an agreement from the Afghan government. He suggested that if no agreement can be reached, he would be comfortable with a full pullout of U.S. troops.

“If in fact we can get an agreement that makes sure that U.S. troops are protected, makes sure that we can operate in a way that is good for our national security, then I’ll certainly consider that,” he said. “If we can’t, we will continue to make sure that all the gains we’ve made in going after al-Qaida we accomplish, even if we don’t have any U.S. military on Afghan soil.”

All U.S. forces left Iraq at the end of 2011 after no deal could be reached to keep some there longer.

Obama, an avid sports fan, also weighed in on the controversy surrounding the Redskins as the name of Washington’s NFL football team. The name has faced a new barrage of criticism for being offensive to Native Americans.

The president said he doesn’t think Redskins’ fans mean any offense by using the name. But he added: “If I were the owner of the team and I knew that the name of my team, even if they’ve had a storied history, that was offending a sizable group of people, I’d think about changing it.”