In an indication of the difficulty of the job, some of the states with delays, like Oregon and Maryland, have been preparing for many months and have political leaders who strongly support the law.

“It makes you wonder about the exchanges that actually have been at this a shorter period of time,” said Jon Kingsdale, a managing director at Wakely Consulting Group, who is advising several state-run exchanges. “Do they even know what their problems are?”

The federal government, which will operate all or part of the exchanges in more than 30 states that declined to create their own, mostly because of political opposition to the law, is having readiness problems of its own. In one example, the Obama administration said on Thursday that small businesses would not be able to buy coverage online through federally run exchanges until November.

Although the exchanges have been able to tap billions of federal start-up dollars and hire companies like Accenture, Oracle and Xerox to help with the work, their task has been highly complex and their time frame tight.

The Web portals for the exchanges have to be able to share information in real time with insurance companies, state agencies and the federal government, which has built a “data hub” through which it can verify the income and citizenship of people applying for subsidies or Medicaid. Each portal has to undergo rigorous testing to ensure, for example, that data will flow properly, that the portal is secure and that it can handle heavy volume. Much of the testing is still going on.

“Everybody is working 24/7,” Christine C. Ferguson, the director of Rhode Island’s exchange, told reporters in a conference call last week. “We are sliding into that date still testing and making sure that we are able to fulfill the promise that we’ve made for Oct. 1.”