Tracfone, which is owned by Mexican billionaire Carlos Slim, said in a statement that it does "not believe that our conduct violated any rules or that the proposed FCC action is warranted."
"We believe that we have the most sound program in the industry when it comes to wireless Lifeline. TracFone has been a leader in both innovative wireless Lifeline services and in preventing program abuses," the company said.
Clyburn is a fierce defender of the agency's Lifeline program, which has come under fire from conservatives as a wasteful government handout. The program is often derisively referred to as the "Obamaphone program," although it began long before Obama took office.
Congress first enacted the Lifeline program in 1985, during the Reagan administration. In 2005, under President George W. Bush, the FCC expanded the program to cover cellphone service.
The program pays for phone service, not the phones themselves. But many companies that receive funding through the program offer free and low-cost phones to their subscribers. The program is funded through fees that the telephone companies pass on to consumers on their monthly bills.
The program has ballooned in size in recent years and there have been widespread reports of abuse and fraud.
In an effort to eliminate waste, the FCC last year toughened its eligibility standards and created a database to ensure that multiple companies were not receiving subsidies to provide service to the same customer.
But conservatives claim the program is still out of control and have proposed legislation to end the cellphone portion of the fund.
Democratic Sen. Claire McCaskill (Mo.) is also leading the charge to pressure the FCC to tighten oversight.
"Ultimately, our objective is to eliminate fraud, waste and abuse, while preserving and promoting the availability of communications services to those in need," Clyburn said. "I will do all I can to ensure that we achieve this balanced result."
The FCC announced the fines late Monday, just hours before the agency was forced to shutdown due to failed negotiations in Congress over government funding.
—Updates to include a statement from TracFone at 2:37 p.m.