At present that is not possible via the API (as the actions which change passwords create new expiration and reset tokens before they send the email) - you're welcome to add it as an idea to community voice and see if others feel the same way -the most popular items are the ones we look at when deciding the scope of releases.
By the way, the expiry time is configurable - heres some text from a document I've been working on:
Log in as a superuser (such as host), and go to host->host settings. Click on the advanced settings tab and then scroll down and click on "Membership management". You'll find a number of settings that affect various member related activities.
The first of these is the "reset link timeout". As hashing is a one-way operation, and once stored a users hashed password cannot be retrieved (e.g. to send out in a password reminder), DNN had to make changes to the platform to support password resets via reset links. Rather than have two systems, one that emailed passwords (via SMTP in cleartext) for sites that used encryption, and one that sent out password reset links for sites that used hashing, the product team made the decision to only use password reset links as they are more secure. Now, when a user initiates an action that used to send out a password (such as registering or password reminders), an email is sent with a password reset link. This link is unique to the user, can only be used once, and also has an expiration date to ensure that it is only valid for a short period of time e.g. in case someone accesses your email, reset links that have been used or expired can no longer be used.
The first setting on this page controls this value, and defaults to 1 hr (60 minutes). It's important to note that this value only applied for actions the user initiates themselves - for actions such as an administrator/host created a new account or resetting a users password, the expiry for those mails is 24hrs. This longer period allows users a better opportunity to respond to the mail by clicking the reset link. If the link is expired, they can request a new one (which will then be valid for the "Reset link timeout" specified under "Membership management"), but the larger timeout for admin/host initiated actions will improve the chances the user can respond to the original email.