Some insurance experts warn that the federal Obamacare marketplace has a month or so to heal itself or risk harming enrollment. Others say it could be months, if not much longer, before the website is free of tech problems.
In the meantime, many insurers aren't waiting for the federal marketplace to get its act together and are directly enrolling customers in Affordable Care Act plans without forcing them twiddle their thumbs on the Healthcare.gov marketplace.
Independence Blue Cross says its own website is seeing considerable traffic. Volume is "about five times the level we normally see during this time period. Via phone, it's three times," said Daniel Hilferty, the Philadelphia-based insurer's president.
Robert Zirkelbach, spokesman for the insurance industry trade group America's Health Insurance Plans, echoed that, saying "our health plans around the country have seen a tremendous volume on their website and on their call centers from day one" of open enrollment on Oct. 1.
(Read more: Obamacare tech woes)
Not all of those visitors are enrolling—yet—but "there is a lot of interest" and "if somebody wants to sign up directly with us, fine," Hilferty said.
Independence, and other insurers, have added a calculator on their website so that visitors can get a rough idea of government subsidies they might qualify to offset the cost of insurance.
The calculators that will give an accurate subsidy amount are on the federal exchange, but the exchange's tech woes have made it difficult to use them. And experts said that the federal exchange isn't likely to be debugged for some time.
'Epic' ecommerce platform
"I think it could easily take up to two years before all these things are working smoothly," said Lisa Carroll, president of the Mosaic Insurance Exchange and the Small Businesses Service Bureau in Massachusetts. "This is just an ecommerce project of epic proportion," said Carroll.
Carroll said the complicated task of getting all facets of the federal health insurance market to interact with each other correctly is made more complicated by rule changes and clarifications that have to be accounted for by software.
"It's an evolutionary process," she said.
Many of the government-run marketplaces were overwhelmed by visitors since the start.
But the persistent lags and difficulties getting through the enrollment process on Healthcare.gov—which is acting as an insurance marketplace for the 36 states not running their own exchanges—have drawn the most attention.
"What was supposed to be 'simple as buying airline tickets on a website' has turned into trying to find a needle in a haystack," said Barry Sloane, CEO of Newtek, a health insurance brokerage for small businesses.
The Health and Human Services Department, which operates the federal marketplace, is working aggressively to fix the site's slow speed, which it blames on too many people trying to create accounts, and check out the prices of plans being offered by competing insurers.
But experts have pointed to software flaws as the main source of problems.
(Read more: Obamacare deadlines)
Sumit Nijhawan, CEO of insurance data integrity provider Infogix, said, "My crystal ball tells me it's going to take anywhere from six to nine months" to resolve those problems. Nijhawan said the problems could get a bit worse before they get better when exchanges start dealing with a large influx of people enrolling before the Dec. 15 deadline for the start of coverage on Jan. 1.
More strains to come
Joel Ario, who headed HHS's health insurance exchange office from 2010 until 2012, told Time.com that government exchanges need to quickly make necessary tech fixes or face serious enrollment problems.
"By November—certainly the middle of November—the sites have to be able to handle major traffic for people to be able to set up accounts and purchase coverage," Ario told Time.
Infogix's chief product officer, Bobby Koritala, said many of the strains will come after people are enrolled and have their eligibility for government subsidies to buy insurance verified.
"The membership subsidies are simple" to handle, Koritala said. Much trickier, he said, will be processing billings, changes in people's incomes and calculating the subsidies that can be used to offset the cost of out-of-pocket expenses such as co-pays.
(Read more: Obamacare exchanges)
Gary Lauer, CEO of eHealth, which operates the Web marketplace Ehealthinsurance.com, agreed that the federal exchange has a short window to solve their software problems.
Lauer's and several other insurance markets are supposed to be electronically connected to Healthcare.gov so they can also sell the subsidy-eligible plans available on the government market. But those connections have been delayed because the government delayed giving the websites the data they need to hook up with it until just days before the Oct. 1 launch.
Lauer said he hopes the connections will be made "within the next couple of weeks." He said, "We're working with some of the engineering people [at Healthcare.gov] but we sense they're up to their ears."
In the meantime, Lauer said, Ehealthinsurance.com is giving visitors to its website an electronic "rain check," and will let them know when they should come back.
—By CNBC's Dan Mangan. Follow him on Twitter @_DanMangan.