Term for using hyperbole to make a softer argument seem more palatable?
There are several cognitive biases which describe why people are often more likely to accept a position after being presented with an unreasonable position.  

Focalism

Focalism or anchoring is the cognitive bias in which humans rely heavily on the first piece of presented information (the anchor) to make subsequent judgments. From the wiki definition:


  For example, the initial price offered for a used car sets the standard for the rest of the negotiations, so that prices lower than the initial price seem more reasonable even if they are still higher than what the car is really worth.


Door-in-the-face technique

The DITF method is a compliance manipulation technique in which a persuader attempts to convince a respondent to agree or comply with an argument by initially making a substantial and unreasonable request, and then when it is turned down, making a second more reasonable request. See Cialdini (1975) for the founding investigation.