WASHINGTON — Milwaukee, Detroit and Philadelphia have done the best among 20 cities competing to sign up people for health insurance under the Affordable Care Act, while Dallas, Denver and Las Vegas are lagging, the White House said Monday ahead of Tuesday’s deadline to enroll for coverage that takes effect on Jan. 1.

A surge of callers temporarily overwhelmed the government’s capacity to enroll consumers on Monday, prompting officials to record telephone numbers so they could return calls later to arrange for coverage.

Federal officials said that people stuck waiting would be given a brief special enrollment period so they could complete their applications and select health plans after Dec. 15, but still get coverage in January.

“We are seeing unprecedented demand,” said Lori Lodes, a spokeswoman for the Department of Health and Human Services, which runs the federal insurance marketplace.