First of all, I'm going to say I don't care about the constitution - I'm not even a U.S. citizen, never been there, even less incentive for me to care. I only care about what is right or not.
If they violated someones rights, their rights are already being infringed upon. Ones rights are already strictly limited when entering prison, but in an attempt to keep them away from society, it bares extreme costs to the society because not only do they sometimes get more inclined to commit crimes after prison time but their prison time along is a huge financial burden.
Forced labor sounds extremely harsh, but you don't have to have them working for 16 hours or anything, just a little while (maybe like a regular day job) - to make it more cost-effective. Their legal rights should not be compromised though, and habeas corpus is very important.
The only objection to this could be a moral one, and I actually agree with that objection, I don't believe in forced labor even in these circumstances, but what better method is there if one actually wants to cut costs.