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Ir's not just that; the IRS lists sharing/borrowoing dependents as one of its Top 12 “Dirty Dozen” Tax Scams. It's a HUGE (or “HUGH;” if you prefer) problem and Santorum wants to compound it w/his ill-conceieved tax plan.
“Share/Borrow EITC Dependents"
“Unscrupulous tax preparers “share” one client's qualifying children with another client in order to allow both clients to claim the Earned Income Tax Credit. For example, one client may have four children but only needs to list two to get the maximum EITC. The preparer will list two children on the first client’s return and the other two on another client’s tax return. The preparer and the client “selling” the dependents split a fee. The IRS prosecutes the preparers of such fraudulent claims, and participating taxpayers could be subject to civil penalties.”
Source Link: http://www.taxhelpattorney.com/articles/common-tax-scams.html
He is advocating tripling the tax deduction, not any tax credit. This policy does nothing to encourage low income families to have more children. It is mainly those families paying a lot of tax who would receive the benefit.
It is key to understand the difference between a credit and a deduction.