The Obama administration said Tuesday that it would provide more time for people to sign up for health insurance if they could show that they missed the Tuesday deadline for applications because of problems with the federal health care website…

“If you weren’t able to enroll in an insurance plan by Dec. 23 because of problems you had using HealthCare.gov, you still may be able to get coverage that starts Jan. 1,” the administration told visitors to the website. “Even though we have passed the Dec. 23 enrollment deadline for coverage starting Jan. 1, we don’t want you to miss out if you’ve been trying to enroll.

“Sometimes despite your best efforts, you might have run into delays caused by heavy traffic to HealthCare.gov, maintenance periods, or other issues with our systems that prevented you from finishing the process on time. If this happened to you, don’t worry — we still may be able to help you get covered as soon as Jan. 1.”

New York and Massachusetts are following the federal health exchange’s lead and extending their sign-up deadlines for coverage starting Jan. 1, those programs’ directors announced Monday afternoon.

Other state exchanges, including the ones in California, Washington state and the District of Columbia, are offering general flexibility for individuals who started but couldn’t complete their applications by the 11:59 p.m. Monday deadline. Residents there will still be guaranteed coverage starting Jan. 1…

New Yorkers now will have until 11:55 p.m. Christmas Eve to choose a plan, said officials, who described “very high enrollment activity” Monday.

Massachusetts residents have even longer, until New Year’s Eve, to enroll and pay their first premium if they are receiving a federal tax credit. Those choosing Massachusetts Health Connector plans who are not eligible for federal subsidies also benefit from the new Dec. 31 date and have through Jan. 10 to pay their initial premium.

“The amazing, ever-expanding deadline? It’s clearly a sign of desperation by the administration to do everything they can to increase the number of people signing up,” said health economist Gail Wilensky, who ran Medicare for President George H.W. Bush…

The insurance industry, too, has pushed back deadlines for payment, with most health plans allowing customers to pay by Jan. 10 and still get retroactive coverage to Jan. 1.

“With deadlines that keep changing, insurers want to alleviate confusion,” said Robert Zirkelbach, spokesman for America’s Health Insurance Plans. “Health plans are going to do everything they can to help consumers with the enrollment process.”

For a law that’s faced automatic Republican resistance from the start, the ball fumbling since Oct. 1 that President Barack Obama has repeatedly acknowledged hasn’t helped.

The president and his aides say every announcement has been the result of being responsive and flexible, trying to make the law work for everyone. But at this point, the administration appears to be demonstrating that it lacks either a full sense of what implementing health care entails, or a full sense of the kind of blowback that each shift in the rules, however small, will generate…

“This latest delay marks the third major change since Secretary Sebelius testified on Dec. 11 when she was asked point blank what changes were in store over the holidays, and she was mum. And yet, another day, another delay,” said Rep. Fred Upton (R-Mich.), chairman of the House Energy and Commerce Committee and a frequent critic of the law. “While the holiday surprises have become commonplace, the latest extension is another disappointment for the ‘most transparent administration in history.’ As we celebrate Christmas and prepare to ring in the New Year, we continue to ask, ‘what’s next?’”

Furman continued: “We’re obviously making — it’s not a Plan B — Plan A is to do the most aggressive enrollment efforts you can, with young people, using social media. You see the insurance companies doing paid advertising. It’s in the insurance companies’ interest to sign these people up.” Beyond relying on a social media campaign, Furman argued, the work done by private business on behalf of Obamacare could be critical. “We’re doing everything we can, but I think unleashing the private sector and the large amounts they’re going to spend on advertising might be even more important,” he said.

Schneider was still curious. “But you have no particular backup plan?”

“There’s a Plan A,” Furman answered. “Which is to enroll as many young healthy people as you possibly can.”

It now seems possible that no one will be paying the mandate penalties in 2014. Having exempted some groups from the mandate already, it will be politically difficult to start enforcing it on others. And, looking further into the future, why should we think Democrats will suddenly crack down and enforce the mandate in the run-up to the next presidential election?

This part of the law is like an unpopular, insecure person at a family reunion, who is walking on eggshells and making concessions right and left for fear of offending anybody. In the age of the Internet, people are used to decentralized systems and maximum personal choice. The mandated elements of Obamacare may look good on paper and they may be necessary to get the plan to work, but they probably can’t survive the public sense they are illegitimate.

Governing in an age of distrust is different than governing in an age of trust. Government now lacks the legitimacy to impose costs on losers, so politicians face unprecedented pressure to create situations in which everybody looks like winners. Government lacks the legitimacy to coerce. People like Social Security, but I bet you that Congress could not pass a Social Security law today. If people were unfamiliar with the concept, you couldn’t pass a bill that said: Government is going to confiscate money from each paycheck and spend it on other things, but don’t worry because you’ll get it back decades from now when you retire.

The erosion of the mandate won’t kill Obamacare over all. It’ll just make it much more expensive for the government.

The individual mandate is the heart of Obamacare. From the president on down, administration officials believe that without the mandate, the system won’t work. So the one thing the public hates most is the one thing Obamacare can’t do without. For many Democrats, voting against the mandate, even delaying the mandate, is tantamount to repealing Obamacare altogether. They can’t do it, no matter what the voters think.

That’s a political problem for Democrats and an opportunity for Republicans. In a private exchange not long after the implementation fiasco began, a senior House aide said GOP strategy is to “separate Obama from Congressional Democrats” on the issue of Obamacare. One way to do that is for the GOP to use its control of the House to force Democrats, all of whom face re-election next November, to re-affirm their support of the mandate.

More than 50 Democrats have arrived in the House since March 2010, when Obamacare became law. Fifteen Democrats have come to the Senate since that time. Will their devotion to a law they didn’t pass be as strong as that of more senior Democrats, who fought the original Obamacare battles?…

Republicans held dozens and dozens of votes on Obamacare in years past when the public had little idea what was at stake. Republicans warned that Obamacare would be a disaster, but voters didn’t know what was coming. Now, they do. Maybe it’s time for the House to start voting again.