Thompson told the commissioners Wednesday that he reviewed the proposal and found many problems.
One obstacle is that the commissioners cannot bind future county commissioners to such a proposal, Thompson said.
Second, Thompson said he does not believe government should get involved in setting up such a service.
High-speed Internet service already is provided in the county, Thompson said. And if the county government gets involved in building the new communications network, it would not be fair to other companies that are already providing such services, Thompson said.
Commissioner Rusty Morgan said he agreed with Thompson.
Last week, the commissioners agreed to perform a study to determine the benefits of developing such a system and Morgan said he believes the county should limit its involvement to the study for now.
"I'm very dissatisfied with how this has been brought up," Morgan said.
Commissioner Greg Corliss supported the proposed network Wednesday, saying he believes the proposal is important to spur economic development in the county.
Jane Peters, executive director of the Jefferson County Development Authority, has said the high-speed Internet service offered through the network could be used to attract high-tech companies to the county. And, traditional companies need high-speed Internet to communicate with suppliers or home offices, Peters said.
Peters told the commissioners Wednesday that the "profits could be tremendous" from such a network.
Once the debt is paid off for the system, it could be a revenue source for local government because other information service companies could pay government to be able to offer their service through the network, Peters has said.
"I still think there is potential here," Peters told the commissioners.
The West Virginia Development Office has been touting the advantages of the network, and Peters told the commissioners she would contact state officials about concerns that were brought up Wednesday.