Wait. Just wait a minute here.
You think if our political class had a solution to the debt problem that they would actually use it? 
They do. It's called "Inflation". The underlying assumption forever has been that inflation will shrink any national debt to a manageable level by taxing everyone through making their "dollars smaller". And the wealthy movers and shakers and political class don't mind this since they tend to preserve their wealth as assets, nor do they rely much on income as a portion of their wealth, rather than as "money", so the assets just inflate along with the money.
That's why the Fed did so much Quantative Easing over the past several years after the 2008 crash, it was only partly because they hoped it would jumpstart the economy (it largely failed) and more importantly, once the presumed recovery would happen, the larger money supply would create inflation, shrinking the national debt. Fortunately. from the standpoint of the little guy who depends on income, and his dollars deflating as slowly as possible, despite all the QE money the Fed pumped, and all the TARP money the fed.gov made various banks and firms take, they all were very cautious and sat on that money and did the minimum with it which sidelined much of it from the economy.
Of course, the fed.gov has shot themselves in the foot too, because the left hand does not know what the right hand does. Because they've been screwing with the Consumer Price Index forever, and have done things like remove non-essential goods that they feel unfairly represent the "true CPI", little things, like food and gasoline, because they were too volatile..
However, in doing that, the "official" inflation rate is curbed too, and the other half of the fed.gov that's counting on inflation shrinking the debt gets screwed.
This has been the subject of debate for several years now. I suppose if it could be proven illegal aliens would solve this country's twenty trillion dollar debt, the politicians would import them by the crateful.
I suspect that this study didn't take advantage of all considerations in their figures if all the illegals, or most of them were deported. And that second-order economic damages, wage inflation over fair-market, rising costs of produce etc. and buisness to business industrial durable goods sectors slumped as construction and other industries were affected would all effect the economy. Just computing the taxes illegals pay directly vs. what the government pays out in services doesn't account for nearly all of it. Just a gut level guess, but I'd say the immigrants are actually a net gain, or at worst a wash, and preventing further economic trouble...
However, that's not to make some case for illegals, it simply underscores that there are other deeper pathologies at work in America. Namely that many of these jobs should/would be filled by our massive, multi-generational, and permanent welfare/SSI-disability underclass. That's where America is taking the double-hit in the shorts. The loss of tax income, and the economic drivers/consumption that comes from these people not being productive self-supporting workers, and from the welfare payouts.
