This won't kill the American dream, it will just change how prices are set on houses.
Tax policy should not be used to encourage or discourage behavior, it should be used to raise revenue. Any change to tax policy that removes behavioral incentives is a good thing. There should be more of it.
Secondly, but most importantly, such a deduction shouldn't be the determining factor when purchasing a house. If you need such a deduction to afford the house, then the house costs too much.