Correction: An earlier version of this story incorrectly spelled the last name of Jason T. Andrew. This version has been corrected.

Ron Kirby, a member of the Tea Party, holds a sign against Obamacare outside the Senate side of the Capitol in Washington, Wednesday, Sept. 25, 2013, in support of Sen. Ted Cruz, R-Texas. (Jacquelyn Martin/AP)

Buying health insurance will be as easy as purchasing a plane ticket or shopping on Amazon, the president has promised.

Maybe, but perhaps not on Tuesday — the day that millions of Americans are supposed to be able to start buying coverage under the sweeping law referred to as Obamacare.

Widespread reports of computer problems and logistical glitches are casting a pall over what many supporters envisioned would 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 sites called “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 T. Andrew, an insurance broker in California. He had planned on Tuesday to get on the state’s online marketplace 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.

Here are how eight people might fare under the ystem that has come to be known as Obamacare.

But he hasn’t been certified by the state to do the work. He hasn’t been able to see the exact rates his clients would have to pay on the marketplace. And he’s not confident that California’s site will be up and running, and fully functioning, come Tuesday. California officials insist the marketplace will be ready, and that 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 aren’t 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 on Tuesday, if they occur, will further fuel Republican attacks on the law’s viability. The program is at the center of a standoff between the White House and Republicans on Capitol Hill that could lead to a government shutdown on the very day the marketplaces are to open and an eventual default on the nation’s debt.

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, 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 Web site.

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 Oct. 1.

“Nobody is going to say we’re not starting on October 1,” said Joel Ario, a health-care consultant who formerly oversaw exchanges at the Department of Health and Human Services. “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 latest poll by the nonprofit Kaiser Family Foundation, just 12 percent of the uninsured know that open enrollment starts Oct. 1.

One problem insurers have pointed out is that there are some errors in the premiums that shoppers would 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 to insurers information about what amounts consumers would 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, President Obama touted the ease with which people will be able to buy health insurance on the federally run marketplace,

“Now, this is real simple,” he said during his speech at Prince George’s Community College. “It’s a Web site 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 would be glitches but predicted they would be few and exaggerated by political foes. “They’ll have their cameras ready to document anything that doesn’t go completely right,” he said.

Joanne Peters, an HHS spokeswoman said: “The Health Insurance Marketplace will open in every state on October 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.

Special troubleshooting teams also will be available around the clock.

Still, Colorado’s marketplace, Connect for Health Colorado, decided to delay certain online functions after testing fell behind. People seeking to buy coverage with federal subsidies in the initial weeks will at some point have to call a hotline to finish the process.

“We don’t feel comfortable with it running automated right now,” spokesman Ben Davis said.

The Colorado marketplace was testing more than 100,000 types of scenarios that it might encounter, ranging from relatively simple situations with individuals to more complex cases involving sprawling families. In the more difficult situations, software that was supposed to determine the size of a subsidy was not always coming up with the right number.

In some places, applicants may run into trouble initially finding people to assist them through the enrollment process.

As of Friday, Iowa had no certified “navigators” — groups and individuals who have been approved to serve as in-person helpers. State officials expect the navigators to be certified by Tuesday.

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.