The White House says the site will be much better but not “perfect.” But it’s got to be better enough to fundamentally change the political narrative that it’s broken. If it isn’t, nervous Democrats will get more nervous, and they’ll start searching for more serious ways to distance themselves from the law they passed.

Vulnerable Senate Democrats have already flocked toward bills allowing people to stay on their existing health insurance plans, and the White House has tried to take some of the steam out of that push with a “fix” of its own. And Hill Democrats have signaled they’re ready to beef up their oversight and criticism of the implementation effort if the site falls short even after Sunday’s deadline.

But their tone once Congress comes back to town will be the best gauge of whether the White House has dodged a bullet—at least for the time being.

“There’s a window here; I’m not quite sure how long it is. The Democratic leaders have given the White House some space to try to work out these kinks,” says Jim Manley, a Democratic strategist and former spokesman for Senate Majority Leader Harry Reid.