Timing is everything. Get the unemployment benefits extended beyond the November midterms and deal with it again during the lame duck session. Obama would rather continue the payments than have voters even angrier that they have no jobs.
No jobs AND not even a pittance of unemployment could lead to one heck of an October surprise in the form of angry mobs.
Well politically letting them expire is a huge loser. Those unemployed voters would blame him even more for being jobless if they were cut off, and who would rally behind Democrats for it? Obama is right about one thing, Bush would extend them too and probably unpaid for too. That was his way.
If he admits the benefits will slow employment as he passes them, that wont help him either. His best political option is demi-god and lie and blame Republicans(at this point this is not a very good 'best' option for him to have.) . Some will buy it. Our job is to throw it all back at him.