The Heritage Foundation is a partisan think tank; it's best to take its publications with a grain of salt.
Consider, for instance: the author mentions that undocumented immigrants have a poverty rate roughly twice that of the general population, yet does not appear to factor this into his calculations about how many people will be able to obtain legal permanent resident status. (LPR status is required in order to be eligible for benefits under Medicare and Medicaid, and one cannot obtain LPR status without paying a $4,000 fine.)
But more importantly, this study only examines one side of the equation. Sure, having more citizens available for government benefits will increase costs. What the author fails to mention, however, is that by bringing undocumented immigrants out of the shadows, the government will also have a new source of tax revenue to pay those costs. Many undocumented immigrants are currently paid "under the table," dodging federal income taxes and
payroll taxes on money they earn working. Amnesty gives them an incentive to start paying into the system (and, by the same token, removes much of the incentive employers have to hire them in place of citizens, since employers will have to start paying taxes for them as well).