Con #1: If you've ever used a debt consolidation calculator on a lender's website, and the results described a payment decrease as a "savings," then the "Con" you need to be most aware of is ... the lender!
Look, just because combining your debts into a single loan will result in a lower payment, DOES NOT mean you will experience a "savings."
Because if the interest rate is higher or the repayment term is longer, you will likely end up paying more in interest charges than if you didn't combine your debts into a single loan.
You see, it's the total cost (loan fees and interest charges) of the consolidation loan that determines if you will save any money, NOT the payment amount.
Con #2: Another potential drawback to consolidating your debts, is that most people I know who have consolidated their debts have done so using a home equity loan (HELOC).
What's wrong with that?
Well, nothing ... unless it bothers you that you are probably converting mostly non-secured debts into a secured debt.
If you fall behind in your payments on a non-secured debt, about the worst that can happen is that you might get harassed by a bill collector.
However, if you fall behind on your mortgage payment, you could end up living in a homeless shelter. If that doesn't bother you, then the home equity loan will probably offer the lowest interest rate for your consolidation loan.
Con #3: A third potential drawback to consolidating your debts, is that it lessens the pain of having lived beyond your means. And without that constant painful reminder of the mistakes you've made in the past, you may not have learned a harsh enough lesson to keep you from getting into trouble again.
Sorry, but I defer to your lender because frankly, they have likely covered every conceivable benefit -- and then some.
I always vote for paying off each debt separately, one painful-reminding payment at a time. If you want to actually "save" money while paying off your debts, I suggest using the rollover method instead (Rapid Debt Reduction Calculator).