Middlesex chairman Mike O'Farrell says he supports the concept of a city-based Twenty20 competition, but has long-term concerns over money and governance.
The county became the first to object to a change in England and Wales Cricket Board (ECB) rules, which would allow the competition to take place.
Essex have since also objected, while Yorkshire, Durham and Sussex are amongst those to give their support.
The rule change requires the support of 31 of the 41 voting members.
"We do support the concept of a new tournament - we're very committed to that concept of reflecting change," O'Farrell told BBC Radio London.
"It is much more to do with how the process is working and what the final outcomes will be, and actually what this means to the longer term structure in the game."
The city-based tournament would involve eight teams and is set to start in 2018, with all first-class counties guaranteed £1.3m by the ECB.
Middlesex do not own their own ground and are instead tenants of the Marylebone Cricket Club at Lord's, which O'Farrell said puts the county in a "unique" position.
"We are very involved in the London boroughs and with schools and other clubs, and we could put that money to very good use there," he continued.
"My concern is for the longer term, we could all sign up for £1.3m a year for four years.
"I worry about year five for county cricket and I worry on behalf of the members, and 150-plus years of Middlesex history.
"That's the debate we're having at the moment, and I'm not sure that the board and I feel sufficiently strong enough to guarantee the future beyond year four."