1: What's the main thing a paramedic does have to do?
2: What's the main thing a paramedic has to do?
Example #1 above is only valid in contexts where the speaker is responding to having been told that a paramedic doesn't have to (isn't required to) do certain things - in which case does must always carry very heavy stress.
Also note that the auxiliary have would almost always carry at least secondary stress, and be pronounced haff with a "hard" vowel endingfinal consonant rather than the soft vowel ofone in have. This is a special use of the verb form to have to [verb] (always followed by an infinitive verb), where it means be obliged to. In Past Tense contexts it's usually pronounced hat rather than had, so arguably it's actually a "different" verb, rather than a specialized sense of the existing verb.
It would require quite an unusual context for #2 not to require at least some level of stress on have (the stress indicating "obligation"). For example, if the conversation was focused on the fact that paramedics have a lot of "idle time" when they're just sitting around waiting to be called out to an emergency, in which case the activities "available" to them (to pass the time) might include things like playing cards together or browsing the Internet on their smartphones.
Another way to illustrate the significant syntactic as well as semantic difference between the "obligatory" sense and the more general case is to consider...
3: I don't have anything to do
4: I don't have to do anything (usually pronounced haff)
...where #3 means there are no (appealing) choices of action available to me (effectively, I'm bored), whereas #4 means there is nothing which I'm obliged to do.
In the above examples, we can tell which sense is intended by the word order, but given a written utterance such as...
5: These are the toys I have to play with
...with no indication of stress or the pronunciation of the final vowel soundconsonant in have, it's ambiguous whether the speaker means...
5a: I must play with these toys
OR
5b: I have these toys available to me [if I wish to play with them]