Technically nothing is pushed out. The authoritative server returns the new value immediately, but each resolver keeps the old answer until its TTL expires. So the delay depends on the TTL before the change, not on a fixed 24 or 48 hours.
Name server changes take longer: NS records in the TLD zone often have TTLs of a day or more, and the registry itself needs a few minutes to publish the update.
Check the authoritative server first. If it still shows the old value, the change was not saved correctly, and waiting will not help.
Example
dig @ns1.example-dns.net example.com A +short; dig @8.8.8.8 example.com A +short