After months of technical glitches and political tumult, a burst of last-minute insurance shoppers illustrated the growing appetite for Obamacare and the enormous challenges ahead in making the massive healthcare expansion work.

On Monday, the crush of consumers prompted the Obama administration to put thousands of applicants on hold and push back another key enrollment deadline to Tuesday. This unexpected move came despite weeks of computer fixes aimed at improving the troubled HealthCare.gov website.

Even in California and other states where enrollment was running more smoothly, plenty of consumers were experiencing snags.

Anibal Manzano, 56, left a clinic in downtown Los Angeles on Monday without signing up because enrollment counselors were stymied by computer delays with the California enrollment system.

The pet groomer said he has never had insurance and wanted to get coverage for himself and his wife. "I'll come back next week and see if that works out," he said.

California officials said some technical headaches were inevitable, but the state website was working well enough to have enabled more than 400,000 people to enroll in private health plans as of Sunday. Nearly 30,000 people were picking out coverage daily, not counting thousands more Medi-Cal enrollees.

"The Affordable Care Act is taking off in California, and that bodes well for the nation," said Peter Lee, executive director of the Covered California exchange. "It's exciting to see a state coming together and say: 'Let's make the Affordable Care Act work. Let's put politics aside.'"

Even with the late surge, national enrollment in private health plans remains well short of the administration's goal of roughly 3 million by year end. Federal officials didn't release new figures Monday.

President Obama said last week that more than half a million Americans had enrolled so far in December using the federal website. That would bring the total enrollment in health plans to more than 1 million as of Friday, including both federal and state-run exchanges. Nationwide, an additional 800,000 people had been deemed eligible for the law's expanded version of Medicaid through November.

Strong enrollment is crucial, particularly among young and healthier policyholders, to keep insurance premiums affordable in the government-run marketplaces and to fulfill Obama's goal of dramatically reducing the number of uninsured nationwide.

"It has been a terrible three months for getting this underway. It's been a real tragedy," said Timothy Jost, a health policy expert and law professor at Washington and Lee University in Lexington, Va. "But I think we are turning the corner and things will go a lot more smoothly for the next three months."

Across the country over the weekend, hundreds of thousands of consumers went online or visited enrollment events to meet a Monday deadline for coverage starting Jan. 1.

Applications will be taken through March 31, when the six-month enrollment window closes. Coverage generally takes effect within a few weeks of signing up.

As the deadline approached, federal officials said, the HealthCare.gov site used by residents of 36 states received 1.2 million visits over the weekend and more than 1 million by late afternoon Monday.

By midday Monday, the federal officials activated a queuing system designed to relieve pressure on the site. Julie Bataille, an administration spokeswoman, said that more than 60,000 visitors had submitted their e-mail addresses to be notified when the site was less busy.

Federal officials and their contractors spent weeks retooling HealthCare.gov after a disastrous launch in October.

In light of the bottlenecks, administration officials extended by 24 hours the deadline to sign up for coverage that will become effective Jan. 1. The White House described the postponement as merely a stop-gap to make sure that no one who is online by midnight Monday would be excluded.

"Anticipating high demand, which we indeed saw starting early [Monday] morning, and the fact that consumers may be enrolling from multiple time zones, we have taken steps to make sure that those who tried to enroll today but had delays due to high traffic have a fail-safe," Bataille said.

Critics of the healthcare law, however, say the latest deadline shift represents another failure by the Obama administration. And many insurers and consumer advocates have bristled at the ever-changing rules that they said sow even more confusion among the public about a complex healthcare overhaul.

"How can anyone make healthcare decisions today knowing that the law may be unilaterally changed again tomorrow?" House Majority Leader Eric Cantor (R-Va.) said last week.