Peter Orszag brought to the White House sterling credentials as a deficit foe. But he will leave next month with the federal budget deficit stuck above $1 trillion.

Mr. Orszag's decision to resign as director of the Office of Management and Budget comes as the Obama administration—and the Democratic Party—begin to confront disagreements between those who believe near-term deficit reduction poses too much risk to the fragile economic recovery and those, such as Mr. Orszag, who say the deficit itself may be a more profound economic...