...dude i'm sorry but the New Deal did not bring the U.S. out of the depression...WWII did...I very much disagree. First, the government is able to borrow at a far lower interest rate than individuals - and can thus obtain capital more readily than individuals in tight credit markets. So, when deficit spending is needed to jolt an economy, it's better for the government to be doing the borrowing than for individuals.
Second, the government is able to address "collective action" problems in ways that individuals - and even the market more broadly - cannot.
Take my favorite example - the paradox of the electric car industry. Part of the barrier to demand for electric cars is the lack of a widespread network of plug-in stations (without which electric cars are only useful for short-distance trips). But part of the barrier to the creation of a widespread network of electric plug-in stations is the lack of electric cars on the road; it's hard to raise sufficient capital to fund the creation of that network when there are not buyers ready to hand - it's a true long-term investment. The government is best placed to address that, by incentivizing the creation of the network so that the short term pain of the investment is significantly lessened. It's the equivalent of the massive highway building project of the 20th century - an investment that needed high-level coordination across many states and municipalities . . . the type of collective action that the market has a hard time providing
Except it's actually not all that fuzzy. Take the Great Depression and the New Deal (the classic example of a government stimulus that worked). The sustained economic free-fall had basically wiped out liquidity, and the resulting fear of future ruin had essentially turned the entire country into "savers" rather than "investors". Relying on the market is all well and good when people are participating in it; when people are withdrawing their capital and sitting on it, the market can't do much of anything at all.