Congress can defund Obama's amnesty order
Even if an agency is self funding, Congress can still direct how the money is spent. The key for the Republicans is to avoid approving an omnibus bill which would allow Obama to shut down the government if he did not like the provision. By separately funding each aspect of government, Congress can send him a spending bill for DHS and if he vetoes it is only shuts down that department.
Congress CAN pull financial rug from under Obama's immigration amnesty: Republicans given boost by non-partisan body
The thorny question is answered: Homeland Security authorities need congressional approval for every dime they spend, even if they collect it as part of a fee charged to an immigrant.