Politically, it will look bad if the extension isn't passed. If Obama or the Senate can't pull a bill or an executive order that will extend benefits, it will make them look bad. Since the mid-term elections are coming up, it wouldn't be easy to be the politician who stood in the way of nearly a million angry Americans that lost their unemployment benefits.
Then, there's the economy. Sure, paying out unemployment benefits would cost employers and businesses money through increased taxes. But what's the cost of not paying out unemployment benefits?
Think of the foreclosures that will transpire if people lose their benefits and can't pay their bills. Think of the lost retail sales that will occur, as the first thing to go is superfluous spending. All of these issues will cost companies and the economy much more money that the benefit payments ever would.
Luckily, the unemployed are going strong. The Tier 5 to Survive movement keeps raging on, and there is a petition out there that will hopefully be delivered to Obama, in which case an executive order extending benefits may be in order.