Anything Obama did would have been "controversial." The GOP made sure of that. Obama's mistake was wasting time trying to work with them. Any fool could see they weren't interested.
That wasn't true for the first 6 months. Most of the GOP officials were taken aback at the magnitude of Obama's victory and his win in states like IN and NC. There was substantial fear that total obstruction would be met with more electoral losses. It was only in the August 09 recess at local town hall meetings that the Tea Party showed it's strength pushing back against those members who sought to compromise with the WH. The August recess also marked the decline in productivity of the bipartisan six Senators working on a compromise on health care reform.
Given that timeline, I still think that Trende's insight that a split stimulus might have been played better is worth consideration.
Not a single House Republican voted for the recovery act. That was in February 2009. The GOP had no intention of playing ball.
