It can. It depends on what exactly your Apex code is doing and how long each callout takes.
Assuming each function makes exactly one callout, the primary governor limit to be concerned about is probably
Maximum timeout for all callouts (HTTP requests or Web services calls) in a transaction: 120 seconds
If you are not changing the default timeout of 10 seconds per callout and are making 2 callouts, you won't hit that, but your description suggests that you probably have increased the callout timeout (the maximum for which is 120 seconds each, meaning two such callouts could easily hit the limit).
Note as well that all other Asynchronous Apex limits will continue to apply, such as CPU time, SOQL query, and DML.
Additionally, if the first method performs any DML after its callout to persist results, your second method won't be able to make a callout because DML has already occurred in the transaction.