AFAIK, there is no way around this utilizing any of the facets of ssh. However, you could easily reach a solution using Expect. I've always dealt with Expect directly (i.e. writing an Expect script), however I know there have been many occasions where the cpan module for Expect has been recommended. Take a look.

Clarification: I am speaking about entering in the password when you receive that prompt so that you can log in and continue your script