I have just perused this quickly and can already tell you there seems to be a lot of fail and fearmongering in this study.
For starters, your thread title tells it all. When you talk about deficits you usually equate it with continual spending and look at spending and revenue, to determine the deficit or surplus. The deficit is added to the national debt a surplus is a reduction to the overall debt.
The way they worded it was that over a "lifetime" it has a deficit cost (total benefits minus total taxes)
of 6.3 trillion dollars, they are technically correct but they could have just as easily said that it adds 6.3 trillion dollars to the national debt over a "lifetime".
It is worded manipulatively so that people will go around telling people that amnesty would add 6.3 trillion dollars to the deficit (like the thread title) which isn't true or at least very misleading. It adds 6.3 trillion dollars to our debt over a 50 year period, not our deficit.
The other thing I noticed quickly is that it stated that the average undocumented worker is 34 years old, and then stated that on average they would receive benefits for, on average, the next 50 years.
That would put their average life expectancy at 84 years. Actual life expectancy in the US is @78 years. In lower income families, that number is closer to 74 years. So in order for that to be even close to accurate they would have to cut out nearly 15% of their estimates. And the life expectancy of lower income families has flat lined over the last couple of decades so it is not rising. Maybe those numbers are explained in the study somewhere.
So with just a quick glance there seems to be a lot of misleading and inaccurate numbers right off the bat even without digging into the numbers or the methodology.