In the meeting, Ms. Palmieri said, officials urged the groups to hold back, at least for the first several days of December, to see how much traffic the website is getting. Ms. Palmieri summarized the message: “Our recommendation is that we expect there to be really high traffic. You shouldn’t be driving traffic.”

If the website again crashes repeatedly, Mr. Obama’s critics are sure to pounce and some of his Democratic allies may become anxious and apprehensive. Since the website went live eight weeks ago, the botched system has become a symbol of what Republicans say is an overreaching, incompetent federal government. The debate about the website’s failures, and the broader role of government, may shape the outcome of next year’s congressional elections.

Aides to Mr. Obama have spent the last several days trying to manage expectations by offering high estimates of potential traffic at the end of the month, and by acknowledging that the system will still have problems in the weeks ahead.

“The system will not work perfectly,” Jeffrey D. Zients, who took over management of the website repair effort, told reporters on Friday. He said the site would be able to handle 50,000 users, but added, “To be clear, there will be times that volume on HealthCare.gov will exceed this capacity.”

Luke Chung, the president of FMS, a database company in Virginia, said building the website to handle 50,000 simultaneous users was “not unreasonable.” But he said the government must be prepared to handle much larger numbers at peak times like Dec. 23, just as the Internal Revenue Services does at the tax filing deadline in April.

In an effort to ease pressure on the website, officials have created what they call a waiting room for times when the site is operating slowly. People can ask the government to notify them by email of a better time to use the site, and they will then go to the front of the line, officials said.

Earlier this fall, the administration had envisioned an all-out push to persuade millions of uninsured Americans to log on to HealthCare.gov to buy insurance.