The political consensus that it is a third rail is probably true, but I still think it is a good idea to separate good policy from bad in the ongoing discussions about tax reform. The argument for it is that home ownership is socially desirable, which is probably true, but the mortgage deduction is a bad way to do it. The deduction subsidizes debt, not ownership, creating incentives for borrowing even when the owner may have cash in the bank, and it also subsidizes home equity loans to purchase cars, or a vacation to the Bahamas. The person who pays cash for a house gets no tax subsidy, and the person taking out a $1 million mortgage gets a much larger subsidy than the person taking out a $200k mortgage, even though the social benefits of home ownership, if they exist, are probably similar for both owners. That is, while it may be socially valuable to have people own a home in the community, I am not sure why it is five times more socially valuable for them to have a mansion instead of a rambler.
If you want to subsidize home ownership, the way to do it is something like a $1000 refundable tax credit for owning a house in which you live. You get the credit whether or not you borrow or pay cash, and no matter the size of your mortgage.