The millions of health coverage cancellation notices that have gone out in recent weeks have thoroughly debunked President Obama's pledge that if Americans like their health care coverage, they can keep it. The president, along with the many other Democrats who made the same promise, is now paying a political price for his words.

But the keep-your-coverage promise was just part of the Obamacare sales job. Obama, then-House Speaker Nancy Pelosi, Senate Majority Leader Harry Reid and top Democrats made all sorts of claims in their effort to convince a skeptical public to accept a complicated, far-reaching national health care scheme. Here are three promises that might cause serious trouble in the days to come:

1) Obamacare will save your family $2,500 a year.

During the 2008 campaign, and as president, Obama promised his health plan would "cut the average family's premium by about $2,500 per year." But Obama and fellow Democrats knew that many premiums would actually go up. Obamacare provides taxpayer-paid subsidies to millions of Americans with which to pay the higher prices, but those without subsidies will have to deal with the problem themselves.

In any event, the savings aren't happening, and the administration has abandoned the $2,500 claim. Obama avoided repeating it when Mitt Romney threw it at him during the 2012 presidential debates. And at a recent Senate Finance Committee hearing, Health and Human Services Secretary Kathleen Sebelius pointedly did not use the figure, even when Republican lawmakers pressed her about it.

"I didn't say they're going down," Sebelius said of health care premiums. "I said the rates are lower than was predicted. And for millions of people in the market, they will actually, for the first time ever, have some financial help paying for their health insurance."

So the promise of $2,500 savings has become a reality of rising premiums, with subsidies for some. It's a broken promise that could prove politically toxic for the administration.

2) Obamacare will create millions of jobs.

In 2010, as Obamacare neared final passage, Nancy Pelosi promised it would be a big boost for Americans looking for work. "This bill is not only about the health security of America," Pelosi said. "It's about jobs. In its life it will create four million jobs, 400,000 jobs almost immediately."

"The health care bill," Pelosi said at another time, "is a jobs bill."

It's not. Yes, Obamacare will create some jobs — there are temporary positions as "navigators," permanent jobs in the IRS and elsewhere to administer the program, and an expanded private health care bureaucracy. But Obamacare will likely cost a significant number of jobs in other areas, and the most optimistic assessments these days are that its effect on employment will be basically neutral.

Pelosi made the claim when Democrats were under attack for taking their attention away from the economy and focusing instead on passing health care reform. Now, her unfulfilled promise could come back to haunt Democrats.

3) Obamacare won't hurt Americans who are already insured.

Obama has repeatedly promised that his plan will make the health care system work "better for everybody." In particular, he promises that the 85 percent of Americans who already have coverage will be basically unaffected by Obamacare, beyond enjoying some of the system's new benefits.

"If you're one of the nearly 85 percent of Americans who already have insurance ... you don't have to do a thing," Obama said in June. "You've just got a wide array of new benefits, better protections and stronger cost controls that you didn't have before, and that will, over time, improve the quality of the insurance that you've got."

It's a simple promise: Most people won't notice much of any change due to Obamacare. And that could be the most potentially dangerous promise of all.

If, as many experts believe, Americans who have employer-based coverage face cutbacks in working hours, or find that their bosses cancel their coverage in favor of sending them to the exchanges, or face higher costs because of Obamacare's requirements, or lose spousal coverage, or have to deal with narrowed provider networks, or lose their jobs altogether — if those things and more happen to a significant number of Americans, the president and his party could face a truly national backlash.

Until Oct. 1, Obamacare was something in the future for most Americans. Now it's becoming a reality. The gap between that reality and the president's promises will determine whether Obamacare can survive.