Buying health insurance will be as easy as purchasing a plane ticket or shopping on Amazon, President Barack Obama has promised.

Maybe, but perhaps not on Tuesday — the day when millions of Americans are supposed to be able to start buying coverage under the sweeping law formally known as the Affordable Care Act but often referred to as “Obamacare” by critics.

Widespread reports of computer problems and logistical glitches are casting a pall over what many supporters envisioned will be a triumphant day for the embattled program. State and federal health officials have said in recent days that some key functions of the online insurance marketplaces will not be ready right away. Some of the consumer guides meant to help people sign up for coverage are not yet certified to do so.

Some people who had planned events in conjunction with the opening of the marketplaces have called them off.

“We just kind of laughed and said, ‘Well, I guess we’ll have to reschedule,’ ” said Jason Andrews, an insurance broker in California. He had planned to get on the state’s online marketplace Tuesday and enroll a couple of people who were excited about the health care law and wanted to be among the first to sign up for coverage.

But he has not been certified by the state to do the work. He has not been able to see the exact rates his clients will have to pay on the marketplace. And he is not confident that California’s site will be fully functioning come Tuesday.

California officials insist the marketplace will be ready and say the brokers will be certified in early October.

Obama administration officials have warned there might be rough spots in the early days. They also have said those problems are not likely to prevent people from signing up for coverage that starts Jan. 1, when many of the law’s benefits and consumer protections kick in.

However, widespread problems Tuesday, if they occur, will further fuel Republican attacks on the law’s viability.

Under the law, more low-income citizens will become eligible for Medicaid, the state-federal program for the poor, while others will receive federal subsidies to help pay their premiums for private coverage bought on the marketplaces. Some of the marketplaces, also called exchanges, are being operated by the states, but most are being run at least partly by the federal government.

Some problems could be worse than mere glitches:

In the District of Columbia, people who use the online marketplace will not immediately learn if they are eligible for Medicaid or for subsidies.

In Oregon, people will not initially be able to enroll in an insurance plan on the website.

In Vermont, the marketplace will not be ready to accept online premium payments until November.

In California, it could take a month for an insurer to receive the application of someone who applies for coverage on the exchange on Tuesday.

“Nobody is going to say we’re not starting on Oct. 1,” said Joel Ario, a health care consultant who formerly oversaw exchanges at the Department of Health and Human Services (HHS). “But in some situations, you may see a redefinition of what ‘start’ means.”

From a practical standpoint, a slow start might not have a big impact on consumers. According to the nonprofit Kaiser Family Foundation, just 12 percent of the uninsured know that open enrollment starts Tuesday.

One problem insurers have pointed out is that there are some errors in the premiums that shoppers will see online. A senior administration official said that such problems are being worked on and that the marketplaces will be ready on time.

But as the launch nears, more delays are occurring. On Thursday, the administration announced a delay in the online shopping system for small businesses and confirmed that the Spanish-language site for signing up for coverage will be delayed until mid-October. Earlier in the week, officials said Medicaid applications will not be electronically transferred from the federally run exchange to states until November.

Jon Kingsdale, former head of the Massachusetts health exchange who is now a consultant to many states about their exchanges, described a particularly worrisome problem. In testing, he said, some exchanges have been unable to immediately send insurers information about what amounts consumers will owe for health plans. The impact should be minimal if addressed in October. “If that isn’t working on an automated basis by the end of October, we’re really in deep doo-doo,” Kingsdale said.

On Thursday, Obama touted the ease with which people will be able to buy health insurance on the federally run marketplace, Healthcare.gov. “Now, this is real simple,” he said during his speech at Prince George’s Community College in Largo, Maryland. “It’s a website where you can compare and purchase affordable health insurance plans side by side, the same way you shop for a plane ticket on Kayak, same way you shop for a TV on Amazon.”

He said there will be glitches but predicted they will be few and that any that crop up will be exaggerated by political foes.

Joanne Peters, an HHS spokeswoman, said: “The health insurance marketplace will open in every state on Oct. 1. As we have said, we expect that adjustments will be needed along the way, and will be ready to address them.” She said that thousands of in-person helpers have been certified across the country.

On the federally run marketplaces, the system for brokers to become certified to help people sign up on the marketplaces has been plagued with problems, say insurance brokers.

The certification site “is constantly crashing. It’s been a complete pain,” said Wes Bissett, senior counsel for state government affairs at the Independent Insurance Agents and Brokers of America.

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