Arthur Laffer think’s its prima facie absurd to think that extending unemployment benefits could reduce unemployment:

No one opposes unemployment benefits as a transition aid for people to get back on their feet and find a new job. Unemployment benefits are a safeguard for individuals down on their luck. But to argue that unemployment benefits actually reduce unemployment is disingenuous at best, and could induce our government to enact policies that have the effect of destroying our nation’s production base from whence all benefits ultimately flow.

Although some partisans may overextend their spin in the heat of political battle, I think for the most part the arguments for improving the economy and extending unemployment benefits lie along different tracks of reasoning. Most people see payments to the unemployed as a compassionate expense to be balanced against efforts to revive the economy.
I will say, though, that I like Mr. Laffer’s suggestion for an alternative stimulus:

Since late 2007 the federal government has spent somewhere around $3.6 trillion to stimulate the economy. That is a lot of money.
My suggestion would have been to take all $3.6 trillion and declare a federal tax holiday for 18 months. No income tax, no corporate profits tax, no capital gains tax, no estate tax, no payroll tax (FICA) either employee or employer, no Medicare or Medicaid taxes, no federal excise taxes, no tariffs, no federal taxes at all, which would have reduced federal revenues by $2.4 trillion annually. Can you imagine where employment would be today? How does a 2.5% unemployment rate sound?

Unfortunately, where government spending is concerned, neither political party emphasizes the greatest economic efficiency. The temptation is too great to convert the money into political currency.