Reports were that the Obama team figured Congress would push the size of the bill up, since that's how things typically went during the Bush years (IIRC the agriculture, energy, transportation, and Medicare drug bills all followed that pattern). They should have sussed out early on from the centrists' rhetoric that it was going to get shaved down, and started negotiating from a higher number.
They also wanted to stay under $1 trillion because it's a Big Round Number, but I don't think it would have mattered. Congressional Republicans referred to it as costing that much anyway, and I seriously doubt more than a small fraction of the electorate accurately remembers the final price tag.
