No.
You get to read all the time about companies outsourcing jobs abroad. Do you often get to read about young startup companies that just started growing and is hiring people? Apparently not. Thats thats not because such a thing is no longer happening but rather because they are happening all the time and so isn't news. When big names in the industry outsource jobs thats big news. Cuz thats doesn't happen all too often, at least not as often as companies hiring people in large numbers.
If outsourcing had been a one way traffic for jobs with the kind of effect media and politicians have been projecting it, US exports would not have increased from $1.2 trillion to $1.4 trillion from 2005 to 2006, 13% increase in just one single year. Surely someone in the US is doing a job, making all that stuff going out for exports. More then a trillion dollar worth of exports! Its not being made out of vacuum by nobody.
What is visible about the issue of outsourcing is the aspect of job loss, whats not so visible is the capital gains thats reinvested back in the economy. You cant see it but its happening all the time. And America’s comparative advantage is not in labour but in capital. Capital gains provided through outsourcing is rejuvenating the economy.
In contrast “illegal immigration” is bringing in more labour surplus of low skilled variety (precisely the kind US doesn't need). In short run more low skilled labour will cost US more then any gains it may provide. In long run however the children of the “illegal immigration” may acquire education and may join the specialised (skilled) labour force, the kind of resource we actually need.