Can a promised to pay be enforceable against an estate?

If it was a written contract to pay and the other side honored its obligations, then it can be enforced against the estate. But if it's not a written contract, the promise is unenforceable. 
There are three things required for enforceability:
1) It must be a contract. A contract requires mutual "consideration"--that is, each party must give or promise something of value to the other. For example, say that A agreed to pay B's mortgage while B in turn either paid A money for that promise (e.g. A needed money now, and agreed to pay a mortgage later in exchange for money now) or gave A something else of value (like some other property; like a patent or trademark; like the right to collect or receive money from a third party; etc.), then you could have a contract. But if A simply promised to pay the mortgage without receiving anything in return, that is a "gratuitous" (or freely made) promise and does not form an enforceable contract: A, or A's estate, can simply decide to not honor it at will. Contracts are enforceable; non-contractual promises are not.
2) It must be in writing. Agreements to pay another person's debt must be in writing--oral agreements to pay another's debt are not enforceable.
3) The person whose mortgage is to be paid must have complied with all his or her obligations under the contract. If A promised to pay B's mortgage in exchange for B paying A money now, then if B failed to make the payment when he or she should have, that failure or breach would absolve A (or A's estate) of their own obligation(s). You can't enforce a contract unless you are in compliance with it.