Groups seeking to block the order must file their cases by Friday. A lottery will then determine which court will hear the challenges to the order.
The FCC's Universal Service Fund was originally designed to subsidize landline phone access in rural areas. Under the new plan, the $4.5 billion high-cost portion of the fund will be renamed the "Connect America Fund" and will be used to expand broadband Internet access.
The program is funded through monthly charges on consumer phone bills.
The agency's order also made changes to the intercarrier compensation rates phone companies pay each other to connect local calls.
The FCC voted for the changes in October and released the full 740-page order in November.