How likely is abolition of the mortgage interest tax deduction?

It is unlikely that it will be completely abolished. It's possible that the deduction terms be amended such that it's less regressive, or otherwise more limited. There are many reasons that it won't become completely abolished, mostly political.

1. Much of the benefits of the deduction are capitalized into the value of property. That means home buyers and sellers are aware of the benefit of the deduction. Therefore, if it were to be completely abolished, home prices would suddenly lose most or all of that value.
2. Additionally, the deduction itself is very beneficial for homeowners with mortgages. They are unlikely to support abolishing this deduction.
3. There seems to be a bias towards home ownership (or at least encouraging such). There's some belief that home ownership is "good" for society, beyond what is priced into the market. Abolishing this deduction would run counter to that goal.

All of these reasons boil down to the current establishment's resistance to abolishing the deduction because they benefit somehow, or believe it will. Even though it may cost 100-200 billion dollars annually in lost tax revenues (Property is very inelastic), it would be political suicide for anyone to pursue the elimination of this deduction.

Personally I believe that it is an inefficient deduction, too regressive, and perhaps ineffective at encouraging home ownership (Remember that the benefit is mostly capitalized into the value of homes), but I am not optimistic that the government will address this issue, even amid severe budget crises.

Morever, The probability is growing more likely as the downward spiral in US real estate values continues unabated.  To wit: "A record 33 percent of existing-home sales were made to cash buyers in February, when an annualized 4.88 million properties changed hands, the National Association of Realtors reported March 21[1]."  

The dynamic is this: What used to serve as a 20% down payment is now very close to an outright purchase price in many areas - especially those cities where price compression has been the greatest, including Las Vegas, Phoenix and multiple areas in both California and Florida.   In these hard hit areas where price compression has wiped out two-thirds or more of the peak value, you may not be able to finance without great difficulty.  

Example: Take a home or condo that was sold at peak for $180,000 and is now listed for $60,000 as a foreclosure.  If a buyer had salted away $36,000 for a down payment based on peak value, why not stretch and just pay cash?  Alternatively, this hypothetical buyer could easily "shrink to fit" his/her requirements to afford a property with fewer features that sold for $120,000 at peak and is now listed for $40,000.

The spectre of a growing number of home buyers opting to pay cash has already had a negative impact on mortgage lenders even without a phase out of the mortgage deduction.  Moreover, taxpayers can deduct the interest paid on first and second mortgages up to $1,000,000 in mortgage debt (the limit is $500,000 if married and filing separately). Any interest paid on first or second mortgages over this amount is not tax deductible.