Currently, there is a fixed constant that limits the total gas usage of a single block to:
hard_gas_limit_per_block = 4000000
With the proto003 fee change, transactions (txs) have minimum gas costs of:
gas_limit : 10100
This means that the maximum number of txs per block is limited to 4,000,000/10100, which is ~396. As blocks have at least a 60 second interval, we have a theoretical maximum of 6.6 (396/60) transactions per second (TPS).
Prior to the proto003 update, higher TPS were possible. It's not clear how the proposed protocol amendment by Nomadic Labs would affect this as no specifics have been released yet. Obviously an increase of the gas limit per block would help to remove this restriction on TPS.