It wouldn't make any difference
If anyone had any doubts about where America sits politically, the last few months should have cleared it up. This is a conservative country. The Obama admin has tried to extend its reach beyond America's comfort level, has been called on it and is paying the price.
I don't beleive going "stealth" now would make any difference. Besides, does anyone imagine that the next Republican govt, when it comes, would find it difficult to strike down that which it doesn't like, especially unpopular legislation?
I still think highly of Obama, but he and his team should have tried to move the ball a few yards rather than going for the hail Mary.