When President Obama signed health care overhaul into law Tuesday, did he fulfill a campaign promise to “bring health care to all?”

The short answer is no. The Congressional Budget Office estimates the overhaul law, as it expected to be amended by House fixes, would eventually cover 32 million more Americans. But that would leave 23 million that would still be uninsured by 2019. So maybe it’s not universal coverage? But who gets left out?

First of all, one-third of the uninsured group, or about 7 million people, are undocumented immigrants who are explicitly excluded. The other 16 million or so aren’t officially accounted for anywhere, but experts have a pretty good idea of who they are.

“Some people will be exempt from the mandate to purchase coverage because they will be unable to find affordable coverage,” Jennifer Tolbert, the principle policy analyst at the Kaiser Commission on Medicaid and the Uninsured, told us. (KHN is a program of the Kaiser Family Foundation.)

That includes a large group of people of limited means who would be exempt from the individual mandate to get insurance. These folks wouldn’t have to pay a penalty for going without insurance if the cheapest available plan would chew up more than 8 percent of their income. People whose income falls below the threshold for filing a tax return with the IRS also get a pass. The problem is that some of these people might earn too much to qualify for Medicaid.

Even among those eligible for Medicaid, not everyone enrolls. “Compliance is never 100 percent,” Henry J. Aaron, an expert on the uninsured from the Brookings Institute, told Shots. Some of them just don’t enroll, because they don’t know it’s available or don’t find it necessary.

Others who are exempt are those who have religious objections, American Indians, or those in between coverage for less than three months, but these categories aren’t estimated to include too many folks overall.

Also some people will remain uninsured simply because they choose not to have insurance and would rather pay the penalties instead, such as young healthy people. “On the average, insurance will be a good deal for the great majority of people, but that won’t be universal,” Aaron said.

But the ranks of those who opt out will thin as time goes on and the penalties increase, he said. The $95 annual penalty in 2014 probably won’t deter too many of those folks who don’t want to buy insurance, but by 2019 when it’s $695 (or 2.5 percent of a person’s income, whichever is greater), more people might decide to buy coverage.

For a sample view of how universal coverage can get ever closer without quite reaching the finish line, take a look at Massachusetts, which in 2006 enacted a law requiring state residents to have health coverage. Even there, 3.5 percent of non-elderly adults are still uninsured, a tiny number compared to the 15 percent national rate now, but not too far off the 5 percent expected by 2019. Just as the CBO projects for the rest of the country, the Bay State reports trouble when it comes to insuring young people and those with incomes under 300 percent of the poverty line, according to the Massachusetts Health Insurance Survey of 2009.

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