Obama administration officials, facing criticism that they are behind schedule in implementing the president’s health-care law, said Tuesday that they have finished a major piece of the technology that will help millions of Americans sign up for insurance this fall.

Federal health officials said they have completed the “data hub,” a complex system that will verify people’s Social Security numbers, immigration status and other information when they log on to government Web sites to buy health plans and apply for government subsidies.

The milestone is a significant victory for the administration, which is battling growing skepticism that it will be ready Oct. 1, when people are supposed to be able to start signing up for health plans under the law, commonly called Obamacare. For months, officials have faced questions about whether the computer systems, which are exceedingly complex, would be up and running in time.

A government watchdog warned this month that a critical security test for the data hub had been delayed and was not scheduled to be completed until Sept. 30. But on Tuesday, officials said they managed to finish that testing on time Friday, calling it a major turning point.

“After over two years of work, [the hub] is built and ready for operation, and we have completed security testing and certification to operate,” said Todd Park, chief technology officer of the United States. “This is an important step in being ready for open enrollment on Oct. 1.”

Officials described the data hub as a network of secure servers that route information. It will connect databases maintained by several federal agencies — including the Internal Revenue Service and the Department of Homeland Security — with other databases maintained in the states.

The security testing, though not as late as feared, nevertheless comes during crunch time for the health-care law, key provisions of which kick in over the next six months.

Starting next year, virtually every American will have to carry health insurance or face a fine; those who lack coverage will have from Oct. 1 to March 31 to meet that mandate.

Whether people comply will depend in part on how easy it is to sign up for an affordable plan, which is one reason why administration officials are aiming to make the process of signing up as simple as possible.

The computer system must also ensure people receive only benefits to which they are entitled based on their income and other factors. If it works properly, the system will be able to fact-check parts of a person’s application in real time, verifying their Social Security number, immigration status and other factors to determine their eligibility for subsidies or for Medicaid, the state-federal health program for the poor.

Critics have raised concerns about the hub, in part because so much of the work is being done at the last minute. Michael Astrue, a Republican and former head of the Social Security Administration who said he supports parts of the law, said it will be impossible for officials to work out the kinks and ensure that it is protected from fraud and hackers in the short time frame left.

“They got a very late start on this, and then they cut corners — and they knew they were cutting corners — to meet their deadlines,” he said. “Whenever you are doing something quick and dirty, the price you pay is problems down the road.”

Dan Schuyler, director of exchange technology at Leavitt Partners, a consulting firm affiliated with former Utah governor Mike Leavitt (R) that is helping several states get ready for Obamacare, called the White House’s news about the data hub “encouraging.”

Still, he said, “most individuals will still experience a rocky enrollment as they go through the online process. It won’t be the seamless and smooth process that had initially been envisioned.”

The hub will be the subject of a hearing Wednesday before a House homeland security subcommittee. Republicans say the hub could be vulnerable to international hackers and identity thieves, among others.

But administration officials said they submitted the hub to rigorous security tests required under federal law, such as ensuring that only qualified people have access to the information it contains, that there are systems in place to monitor it for unusual activity and that there is an ability to quickly respond to problems.

They would not disclose some specifics, however, for fear of revealing too much to potential attackers — including those who may be ideologically opposed to the health-care law and want to interfere with the Oct. 1 launch of the market­places.