Another problem with big government solutions to economic problems is that ALL economic growth comes from small businesses. Small businesses don't do business with the government. At least not new startups. The only thing government can do to promote the growth of small businesses is to get out of the way. Overmuch bureaucracy stifles the kind of creativity needed to make a more prosperous world.
The government can only cultivate an atmosphere where creativity can work freely. They could not have said to Bill Gates in the 70s, 'We think you have a good idea and will give you money to go forward.' Gates would never have amounted to anything had that happened. He had to earn his success to actually achieve it. (I know that sounds a little circular in my reasoning, but I mean it.)
To cultivate a creative atmosphere, there should be a clear set of rules to play by and a limited scope of government so that it is not perpetually gobbling up everything that moves.
Businesses big enough to deal with the billions the government doles out are no solution for a sluggish economy. The very nature of big businesses is that they seek to do more with less. Job one in big business is to increase productivity. So if a big business can do the same jobs with a 10% smaller workforce, they need to either find new things for that 10% to do or cut the workforce.
Growth is a bottom-up, individual, community centered process. Government spending, massive projects, roads, bridges, etc. will never do anything to increase the hiring of a small business. Not the kind that increases national productivity.
I may carve out one exception, and that is some high tech research. The government has more resources for things like that, but the results need to be made available to entrepreneurs and startups so they can come up with new and innovative uses for the technology. But even that I would rather have funded privately.