No, it shouldn't be put up for sale, it should be returned to the states from which it was stolen.
States should control their own lands, and be able to use the resources to bolster their economies. But OTOH, as a sportsman who's lived in a state with an abundance of public lands (Idaho), and many that had very little public land (most recently Texas), I'd have to caution against the wholesale selling off of newly-acquired land to private interests.
There's a lot to be said for not having get permission from a landowner to hunt on his land, or bumping into other hunters every five steps on tiny WMAs, such as they have in most Eastern and Southern states. In Idaho, literally all you have to do is get your required licenses and tags, then find some NFS or BLM land, and you're hunting.
Rotating leases may be the way to go, as long as timber and mining companies restore the areas before they move on to the next. If something like this is in the cards under the Trump administration, I applaud it. But sportsmen have to be wary and active, pounding their state legislators, if they want to ensure they still have a place to hunt.
Scouts Out! Cavalry Ho!
you are4 correct- i misspoke- hopefully trump will give the land back to the states- The problem with government ownership of any kind though is that it severely restricts usage- but the risk as you point out, of private is that it gets shut off completely-