" Capping mortgage deduction will hurt the housing "
Not so. Eliminating the mortgage deduction will reduce home prices, which will entice more buyers, which will restore the housing market. This has been demonstrated in other markets that eliminated these types of artificial supports. Remember, the purpose of the deduction, and other housing market stimulii, is to PREVENT prices from dropping.
The gov't started the housing market mess when it first started meddling many years ago. The gov't has done nothing but cause distortions in the housing market. When the gov't stops meddling, we'll return to a healthy free market.