Even if the US made all 20 million illegal immigrants legal it would still mean that the US has a foreign born population percentage of less then 20%.

298,444,215 (source CIA Factbook)
Foreign born population 10.4% (source NationMaster)
20,000,000 would add another 6.7% to the foreign born population.

So you would have a total foreign born population percentage of 17.1%

Canada has a foreign born population of 17.4%.

Australia has a foreign born population of 23%, a health care system for all, a government surplus... and as for trade we have a trade surplus with the Chinese, export camels to Saudi Arabia, export rice to South East Asia and export Vodka to Russia...

In short I don't think the American economy would collapse if it took on a larger amount of immigrants.

However any country has the right to decide whom they will let in to become a tourist, resident or citizen.