Proof
The unemployment rate is worse than when the stimulus was enacted and that's the facts.
Your mistake is to say job losses didn't immediately end the day the stimulus was enacted. That is obviously ridiculous. Since I don't know you I will assume you are just not applying your thinking cap, vs being deliberately misleading.
The economy was in a free fall when Obama took office and was losing 700k+ jobs a month! The first stimulus money wasn't even spent until September 2009. Some is still being spent today.
The nonpartisan CBO states the stimulus stopped the job losses and by the most conservative estimates added at least 1.5 million jobs.