A lot of state school land has been sold in the past 100 years when the proceeds had to be used exclusively for education. With the proposed transfer there would presumably be no restrictions on what the money could be used for. It could be used for debt service, highways, welfare, new buildings, salaries and who knows what. It could turn out to be a spending spree at the expensive of public land recreationists!!
In all honesty I don't think it would happen overnight, but we would almost certainly be headed in that direction. In 75 to 100 years, some western states may not have much more public land than the Eastern United States (except for the western parks). If history provides any clue, states like Nevada and Utah would likely be most aggressive in selling their land. States like Montana and Colorado would likely be less aggressive. That is my guess under current political/financial conditions. Who knows what political/financial conditions might exist in 25 years, 50 years, 75 years? One thing we can be sure of: If the states get control, greed will eventually prevail!