Blue or red, a majority of states have exceeded their health care sign-up targets under President Barack Obama’s law — something that would have been hard to imagine after last fall’s botched rollout of insurance markets.

But the administration’s final numbers, released Thursday, also expose shortcomings, including subpar enrollment among Hispanics, the nation’s largest minority group and also its least insured.

Still, strong state-by-state performance indicates that the health care law is making inroads around the country, even as Republicans insist repealing “ObamaCare” will be a winning issue in the fall congressional elections. An Associated Press analysis of the numbers found 31 states met or exceeded targets set by the administration before the insurance exchanges opened. Twenty of those are led by Republican governors, many of whom were hostile to the program.

The Health and Human Services Department said 8 million Americans chose a health plan through the new insurance markets in the first year of the historic health care overhaul. Some 4.8 million more gained coverage through Medicaid and children’s insurance programs. A surge in enrollments since March 1 doubled sign-ups in some states, including Texas, Georgia and Florida.

“There is reason to be optimistic about what the law can deliver, both in terms of coverage and affordable insurance options” said Andy Hyman of the nonpartisan Robert Wood Johnson Foundation. “In time, it will become part of the bloodstream of our health care system.” Hyman is a senior program officer working to expand coverage.

With Republicans vowing to make the failures of the law a main theme of their midterm election push, the Obama administration will need to convince the public it has been a success. A recent administration announcement of the 8 million sign-ups failed to move public opinion much, with negative views of the law more common than positive ones. But polls also have found that Americans don’t want the law repealed, preferring that Congress work to improve it instead.

Younger and healthier than the U.S. population as a whole, Hispanics had been viewed as crucial to the success of Obama’s coverage expansion. But the final count was disappointing. Hispanics account for 14.5 percent of those eligible for coverage on the new health insurance markets, but they represented 10.7 percent of the actual enrollees who also volunteered their race or ethnicity, the government reported.