Senate Democrats took their newfound momentum for health reform into closed-door talks with White House aides Wednesday but still faced a months-old problem: centrist Democrats who aren’t sold on Obama-style reform even now.

If Democratic leadership hoped Republican Olympia Snowe’s decision to cross party lines Tuesday would inspire her fellow middle-of-the-roaders, they were mistaken.

And the moderates’ reluctance to commit showed just how far health reform still has to go, despite getting a boost from Tuesday’s Senate Finance Committee vote...