Saying that Roosevelt tried to "stimulate the economy with government investment near the end" of the Depression is a little misleading.
So is Krugman's statement about Hayek arguing, "in the depths of the Depression", against credit expansion.
This makes it sound like we were in the middle of the depression -- without any government intervention yet -- and suddenly the State decides to expanding credit. This is far from the truth. By the middle of the depression, say 1936, the government had already been intervening and expanding credit for seven years. Though I'm sure Hayek and Mises spoke out against such intervention on day one, anyone with half a brain would speak out against a policy that hadn't been working for seven years.
Hoover, like Bush, implemented massive government interventions. Both Hoover and Bush somehow get labeled as Economic "do nothings", but check Hoover's record: after the crash in 1929 he implemented massive trade tariffs (Smoot-Hawely), signed a "Home Loan" act to encourage more houses and protect against foreclosure (sound familiar?), raised income tax, raised corporate taxes, signed the "Emergency Relief and Construction Act" to fund massive infrastructure projects (like the Hoover Dam), etc...
Then, after Hoover's interventions, FDR came along and continued intervening with even larger, New Deal, programs.
Krugman's point of view does seem to be that FDR's New Deal started too late, but he, and other Keynesians, never explain why Hoover's 3+ years of interventions just made things worse. I'm with the Austrians on this one - If the State stayed out of the economy, these depressions and down-turns would fix themselves MUCH quicker.