Obama believes that a balanced budget is something to worry about in the future, not during the conflagration. Among the advantages he has that Roosevelt lacked is the fundamental assumption that government must act when the private sector falters -- the exact opposite of '30s thinking, which, as UC Berkeley economist J. Bradford DeLong has written, held that recession and depression were "good medicine" for the economy. Roosevelt's policies, as it happens, are what drove this notion out of government.
Not that it has entirely disappeared: Before the Senate passed the stimulus bill, it was tinkered with by a coalition of Republicans and "moderate" Democrats to shave it by $100 billion or so. They cut out $40 billion in aid to fiscally crippled states, $20 billion in school construction, and billions more for food stamps and other relief programs, a cheese-paring approach designed to secure three Republican votes.
This achieved so little in economic terms while raising the prospect of more unemployment and more household pain that it looks like something designed strictly for show; in any event, Obama has hinted that he may seek to restore the cut provisions.
In 1933, the British economist John Maynard Keynes wrote an open letter to FDR exhorting him to take a then-novel approach to crisis. In the past, he wrote, it was thought that a government was justified in borrowing only in wartime. FDR had a unique opportunity to borrow for good -- "in the interests of peace and prosperity" instead of "the purposes of war and destruction."