Software problems with the federal online health insurance marketplace, especially in handling high volumes, are proving so stubborn that the system is unlikely to work fully by the end of the month as the White House has promised, according to an official with knowledge of the project.

The insurance exchange is balking when more than 20,000 to 30,000 people attempt to use it at the same time — about half its intended capacity, said the official, who spoke on the condition of anonymity to disclose internal information. And CGI Federal, the main contractor that built the site, has succeeded in repairing only about six of every 10 of the defects it has addressed so far.

Government workers and tech­nical contractors racing to repair the Web site have concluded, the official said, that the only way for large numbers of Americans to enroll in the health-care plans soon is by using other means so that the online system isn’t overburdened.