The Democratic position is that similar worries were heard before the IRS was instructed to implement the Earned Income Tax Credit, yet the program ended up running relatively smoothly.
If you define 'relativley smoothly' as only slightly better than a coin flip in regards to accuracy then read no further.
This Department of the Treasury compliance study reveals that 49.5% of all returns filed claiming EITC overreport the amount of credit entitled. This results in $9.9 billion (with a B) in unrecovered claims. Anecdotally, there are numerous stories of taxpayers 'buying' social security numbers of children they don't have in order to falsely claim the credit for which they don't qualify.
Statistics back this up. According to The Earned Income Tax Credit and Illegal Immigration - A Study in Fraud, Abuse, and Liberal Activism, the EITC which originated as an anti-poverty program, has seen returns claiming benefits grow at a rate 25 times faster than the poverty population over the past two decades. That strongly suggests that this program is anything but realtively smooth.
Than again, maybe that coin the IRS uses is 'Heads the government wins, Tails the taxpayer loses'!