Will Passing a "Signature Achievement" Help Democrats in the Polls?

With Obama's job approval ratings trending below 50%, and health care looking like it may settle into the 30's, Democrats are rallying moderates to health care reform with the following narrative:  sure, passing this may be unpopular, but failing to pass it will be even more unpopular!  The only problem is, Brendan Nyhan suggests that this isn't, like, true.