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The first six-month window for Americans to gain health insurance under the Affordable Care Act closed on Monday with large numbers of consumers speeding to get coverage at the last minute. Some of them encountered obstacles as, the main enrollment website, stumbled on and off throughout the day.

Union halls, shopping-mall kiosks and insurance company lobbies across the country were jammed with people racing to get insurance on the final day before the law required most Americans to choose health insurance or risk a financial penalty.

By the time President Barack Obama appeared Monday evening on "CBS Evening News," he sounded relieved. "We admittedly had just a terrible start because the website wasn't working," Obama said, referring to the site's rocky beginnings. "But given how gloomy I think everybody's assessment was back in the middle of November, I'd say that we're on our way to making sure that no American ever has to go without health care."

Health officials said that, by 4 p.m., 840,000 people had phoned in to a network of call centers across the country — about 300,000 more than the total for any other day since the federal insurance marketplace and 14 similar state ones opened on Oct. 1.

The outpouring of last-minute interest reinforced arguments by the Obama administration and its allies, made since the law was enacted four years ago, that it would become popular once Americans had a chance to get the new health plans that it spawned — and, in most cases, with federal subsidies to help pay for them.

Still, as the deadline arrived, fresh evidence emerged that the law, which has set in motion the broadest changes to the U.S. health-care system in nearly half a century, remains mired in a wide partisan divide. A new Washington Post poll indicates that three in four Democrats support the law — a rise of 11 percentage points since January — compared with one in five Republicans.

On the last day of sign-ups, was inaccessible to new customers — and early on, to anyone at all. Instead of opening at 5 a.m. as scheduled after a routine maintenance period, the website remained closed until after 8 a.m. because of a software problem. Then, starting shortly after noon Monday, visitors to the website were greeted with a screen saying, "We need you to wait here, so we can make sure there's room for you to have a good experience on our site." The screen invited users to leave email addresses so they could be contacted when the volume lessened, although it was unclear whether that would be later Monday or after the official deadline.