I don't know what sort of bizarre methodology they are using over at the Washington Times, but no one else on the planet is claiming any such thing. Not even staunch fiscal conservatives
Anytime anyone tells you that any other part of the US budget is bigger than defense, they are lying. Maybe I misunderstood, and the issue is just the jump in spending rather than the total amount, but even that seems doubtful. Military spending only goes up, and always dramatically so.
More than likely, the Washington Times considers anything useful that the government does as "welfare". Curiously, I doubt they consider the bank bailouts as welfare.
Anyhow, the federal budget is an unmitigated mess, that much is certain.