I'd not say impossible, but given the current attacks and key sizes, ECC 256 signatures are considered safe for the next 20 years.
Now let's assume there's a sudden mathematical breakthrough that allows people to reverse ECDSA, RSA, and other friends based on modular arithmetic - first, you'll have bigger issues to solve (banking cards and biometric passports use similar algorithms
), moreover bitcoin is a more difficult target as you could likely issue new keys faster than the attacker can break them.