Indeed - basically a transaction to "execute" a script will be charged per "step" of execution (we can't tell how long a script will run as they will be "Turing complete"). If the payer hasn't provided enough fees then the script effectively "stops" at whatever step it is currently on (and can be resumed at a later point in time if a new fee paying tx asks it to).

There are also most likely going to be some basic limits as to the max. number of "steps" that a single forger would have to execute otherwise some paying an enormous fee to an "infinite loop" script could bring the network to a grinding halt.