WASHINGTON — Already under fierce attack from Republicans over the new health care law, President Obama now faces broad and mounting Democratic concerns that the troubled start of the insurance program will cut into the political benefit the party received from the government shutdown and cost Democratic candidates in next year’s midterm elections.

Senate Democratic leaders summoned the White House chief of staff, Denis R. McDonough, on Thursday along with the official most responsible for the troubled health insurance website, Marilyn Tavenner, and the person entrusted to fix it, Jeffrey D. Zients, for a closed-door venting session. That followed a meeting on Monday between Vice President Joseph R. Biden Jr. and worried House Democratic freshmen in the office of Representative Steny H. Hoyer of Maryland, the No. 2 Democrat.

It appeared that the White House would have to do more to reassure Democrats who emerged from the 16-day government shutdown confident of their political fortunes, only to see Republicans roar back on a wave of anger over the health care law.

“People are anxious,” said Senator Richard J. Durbin of Illinois, the No. 2 Democrat.

“I don’t think there’s confidence by anyone in the room,” said Senator Jeff Merkley, an Oregon Democrat up for re-election next year, as he emerged from the closed-door meeting in the Capitol. “This is more a show-me moment. We were all confident that the system was going to be up and operating on Oct 1. And now we’re not confident until it’s real.”