WASHINGTON — President Barack Obama gave a consumer-friendly defense of the health-care law Monday and assured the country that the problems many have faced while trying to enroll in new insurance plans would be fixed quickly.

At the same time, Obama admonished Republican critics of the federal insurance exchange and its implementation, saying that “it is time to stop rooting for its failure.”

The president’s address reflected the rising anxiety within the administration over the widening problems with the exchange’s enrollment process, namely through a federal website that has shut out many consumers looking to buy insurance plans before the benefits take effect on Jan. 1.

A Washington Post-ABC News poll released Monday shows that a majority of Americans — 56 percent — believe flaws with the website reflect larger problems with the health-care law, an alarming trend for the administration. But more Americans also support the law despite the enrollment issues, with 46 percent saying they support the law now, compared with 42 percent who say so last month.

In his remarks, Obama was clear about his disappointment with the site’s launch. “There’s no sugarcoating it: The website is too slow; people have been getting stuck during the application process,” he said. “And I think it is fair to say that no one is more frustrated by that than I am.

“There’s no excuse for the problems,” he added, “and they are being fixed.” He said the government is “doing everything we can possibly do” to repair the site, including 24-hour work from “some of the best IT talent in the country.”

Speaking in the White House’s Rose Garden, surrounded by a handful of guests who he said have benefited from the law, Obama served as chief salesman for the three-year-old Affordable Care Act. He emphasized the benefits that have taken effect and played down the faulty website. In outlining the health-care changes under the new law, Obama said twice that “those do not depend on a website.”

As he insisted that problems would soon be fixed, Obama also highlighted alternative ways to apply for the health plans. Consumers can buy insurance through the exchanges “the old-fashioned way, offline,” he said, including through call centers or in person.

But the political and practical mood of the president’s address reflected problems with the website that go beyond the technical issues that have been outlined by administration officials and that Obama emphasized Monday.

The growing concerns over the flawed site — and the slow progress in addressing the problems since its rollout three weeks ago — have become a focus of Republican criticism in the aftermath of the government shutdown. Early on in that political standoff, Republicans demanded defunding or delaying the health care law, known informally as Obamacare, in return for keeping the government open.

Addressing the opposition party Monday, Obama said, “I realize Republicans have made blocking the Affordable Care Act their signature policy idea. And I think, with the problems with the website so far, they are likely to go after it even harder.”

But, “we did not wage this long and contentious battle just around a website,” he said. “We waged this battle to make sure that millions of Americans in the wealthiest nation on Earth finally have the same chance to get the same security of affordable quality health care as anybody else.”

White House officials said Monday that the administration is not considering delaying the law’s individual mandate, which requires that most individuals have health insurance by March 31 or pay a fine, because of the online enrollment complications.

In the budget fight, Republicans sought a year delay in the requirement but eventually gave up. Jennifer Palmieri, the White House communications director, told MSNBC Monday that delaying the individual mandate is “a hypothetical we don’t expect to encounter.”

Congressional Republicans have called for the firing of Health and Human Services Secretary Kathleen Sebelius over the enrollment problems. Several have demanded that Sebelius testify before Congress this week on the law’s implementation, including House Speaker John Boehner, R-Ohio.

The agency’s spokeswoman said Monday that Sebelius would not testify at a Thursday hearing because she would be out of town.

In a statement issued Monday after Obama’s address, Boehner said that “Americans didn’t get any answers from the president today, but the House’s oversight of this failure is just beginning.”

Sebelius, Boehner said, “must change her mind and appear at this week’s hearing in the House. With more than one trillion taxpayer dollars being spent on a completely defective program, Congress is going to get to the bottom of this debacle.”

The Department of Health and Human Services announced Sunday that 19 million people had visited HealthCare.gov since the beginning of the month, although the administration has yet to release figures on how many have signed up for health insurance through the exchange.

On another level, the problems confronting Obama’s signature piece of domestic legislation undermine the broader argument he has made throughout his presidency, that government is capable of working effectively to improve lives. He has been receiving daily briefings on the implementation process, which will be a key part of his domestic legacy.

“No one is madder about the website than I am, which means it’s going to get fixed,” Obama said to applause.

He reiterated that the Affordable Care Act should not be perceived solely as a website, although easily enrolling the uninsured is a central element of the law. He noted other new benefits from the law: that people younger than 26 can remain on their parents’ health-care plan; that mammograms and birth control are free through employer plans; and that premiums are declining in some places for those already insured.

“You may not have noticed them, but you’ve got them,” Obama said. “They are not going anywhere. And they don’t rely on a website.”