WASHINGTON — The nation’s largest minority group risks being left behind by President Barack Obama’s health-care overhaul.

Latinos account for about one-third of the nation’s uninsured, but they seem to be staying on the sidelines as the White House races to meet a goal of 6 million sign-ups by Monday.

Latinos are “not at the table,” said Jane Delgado, president of the National Alliance for Hispanic Health, a nonpartisan advocacy network. “We are not going to be able to enroll at the levels we should be enrolling at.”

That’s a loss both for Latinos who are trying to put down middle-class roots and for the Obama administration, some experts say.

Latinos who remain uninsured could face fines, not to mention exposing their families to high medical bills from accidents or illness. And the government won’t get the full advantage of a group that’s largely young and healthy, helping keep premiums low in the new insurance markets.

“The enrollment rate for Hispanic-Americans seems to be very low,” said Brookings Institution health-policy expert Mark McClellan. “It is a large population that has a lot to gain … but they don’t seem to be taking advantage.”

The Obama administration says it has no statistics on the race and ethnicity of those signing up in the insurance exchanges, markets that offer subsidized private coverage in every state. Consumers provide those details voluntarily, so federal officials say any tally would be incomplete and possibly misleading.

But concern is showing through, and it’s coming from the highest levels.

“You don’t punish me by not signing up for health care,” Obama told Latino audiences during a recent televised town-hall meeting. “You’re punishing yourself or your family.”

Like a candidate hunting for votes in the closing days of a campaign, Obama was back on Latino airwaves yesterday as Univision Radio broadcast his latest pitch.

“The problem is, if you get in an accident, if you get sick, or somebody in your family gets sick, you could end up being bankrupt,” the president said.

Only last September, 3 in 5 Latinos supported the national overhaul, said the Pew Research Center. Approval dropped sharply during October, as technical problems paralyzed the health-care rollout and the Spanish-language version of the HealthCare.gov website. Latinos are now evenly divided in their views.

A Gallup survey recently showed tepid sign-up progress. While the share of African-Americans who are uninsured dropped by 2.6 percentage points this year, the decline among Latinos was 0.8 percentage point.