I think what you want is a welfare state, not socialism.

Socialism is not necessarily cuddly. "To each according to his contribution" is the one sentence description of it after all. I want socialism, because it's "to each according to his contribution" but "to each according to his contribution" isn't obviously this nice cuddly we-take-care-of-everybody type thing.

I'd call the New Deal an attempt to bring discipline to go from capitalism to free markets, to control excesses, prevent monopolies and otherwise preventing people from locking down the economy so that there can be competition, and that's a goal compatible with socialism, because it does bring us closer to "to each according to his contribution" but it isn't an attempt at creating socialism, but of breaking capitalism down to create a market economy with free markets (capitalism is not a market economy, capitalism is the accumulation of capital by some to the exclusion of others, so capitalism and a market economy with free markets are actually things that are extremely incompatible).