My supervisor tells me that they are going to require the exempt employees to punch once a day to tell that we are at the job.

I thought as soon as you punched you were considered hourly and overtime applies.

Is this legal?

Yes, it's legal. There are any number of reasons why an exempt employee's hours might need to be tracked: to determine eligibility for benefits, for security reasons, etc. Punching a clock is one way to do so.

Sorry, but you thought wrong. Punching a clock does NOT automatically make you non-exempt or eligible for overtime.

Now, if you find that your salary is affected by what's on the clock, that's a different story. But as Marketeer points out, there are any number of valid reasons why an employer would track the hours an employee (even an exempt employee) works.