Under the regulations published last August, colleges must have at least one student governor and may have up to three.
But an NUS survey has found that almost one in three colleges is refusing to comply with the rules.
Mark Atkinson, NUS vice-president for further education union development, said: "The NUS wants full compliance and, if naming-and-shaming colleges is what it taes, then we will take on that watchdog role.
"Some of the excuses we heard were as bad as 'my dog ate my homework'. We will happily help colleges run elections, if that is the only real barrier to compliance.
"We also want to praise colleges who have taken two student governors on to their board and we are still waiting to congratulate the first college to have three," he said.
The NUS survey found 23 colleges with two student governors, and 206 with one. It polled 315 out of 460 colleges, and 22 failed to respond.