Population growth alone doesn't help an economy ---definitely not when the growth is in the welfare class. Here we have have increases in population at the same time jobs are leaving the country. Even in the good jobs what good is there when an American is laid off so an H1-B visa immigrant is hired to take the job? Good jobs are the answer to a bad economy.
These are good points you've raised, but I was referring to economic principles in general and not just the U.S. situation in particular.
Consider this micro-example of a tiny "economy" and how it could grow . . .
Imagine an "economy" that consists of three players: 1) a farmer who grow wheat, 2) a general store owner who buys the farmers wheat to sell to the outside world and who buys other products from the outside world and sells them to the farmer, and 3) someone who owns a freight shipping company that provides the store owner with access to the outside markets.
This economy can only grow by increasing the local population or increasing the productivity of one or more of the three players involved. This can be illustrated as follows:
1. The economy will grow if another farmer moves into the area (population) or if the one farmer increases his crop yield through automation (productivity).
2. The economy will also grow if another storekeeper with different product lines opens shop (population) or if the existing storekeeper increases his storage capacity to handle more grain (productivity).
3. The economy will also grow if a second freight carrier with access to new markets gets involved (population) or if the one carrier improves productivity by using newer, more efficient equipment.
No matter how you look at it, these are the only ways the economy will grow. If a squatter sets up camp on the farmer's field and survives by pilfering goods from the storekeeper, then there is no growth involved even though the population has increased. If a government bureaucrat comes along and orders the farmer to give 10% of his crop to the squatter (welfare case), then there is no growth.
But even if the farmer hires manual labor to work in his fields, there will be no real "growth" unless the cost of the labor is less than the additional yield that he can get from having the extra help in his fields. This, I think, goes along with what you were saying about the unskilled immigrants.
And good jobs might seem like the answer to a bad economy, but the jobs have to come from somewhere. A shrinking job base is often a symptom of something fundamentally wrong with the economy, not the other way around.