The records include information on which groups pay for political ads and how much they are paying.
The proposal would also require stations to maintain a database of the sponsorship identifications that political ads are already required to disclose on air.
Transparency groups say the rule changes will increase transparency and make it easier for the public to find out information about political advertising.
The National Association of Broadcasters argues the changes will be an unreasonable burden on TV stations.
In his letter, Burr asked the FCC to explain how it calculated the estimated cost of the proposed rule. He questioned whether the FCC has the budget to maintain the online database of TV station information.