But for the recently completed open enrollment period, sign-ups for the state marketplaces rose a disappointing 12 percent, to 2.8 million people. That compared with a 61 percent increase for the federal exchange, to 8.8 million people, according to Avalere Health, a consulting firm. States with the smallest enrollment growth are among those facing the greatest financial problems.

Most exchanges have operating budgets of $28 million to $32 million. One of the biggest cost drivers is call centers, where operators answer questions and can sign people up. Enrollment can be a lengthy process — and in several states, contractors are paid by the minute. An even bigger cost involves IT work to correct defective software that might, for example, make mistakes in calculating subsidies.

“A lot of people are going to want to know: What happened to all those taxpayer dollars that went to these IT vendors?” said Sabrina Corlette, project director of Georgetown University’s Center for Health Insurance Reforms.