Clearly more data is needed-- how much of a demographic exists where "The only thing we agree on is that those people (congress, senate, et al) need to be drawn and quartered!", is shared between all political alignments? You don't need agreement on which congress critters to draw and quarter, only that the mob gets to draw and quarter members of congress.
Once you cross that threshold, the angry mob will form, and bad things will happen.
If you divide the nation in to 3 piles-- Democrat, Republican, and Unaffiliated-- and get 1/5 of all 3 pools-- you end up with the same statistic.
EG-- start with 100 people-- divide 3 ways so that each group has 33 members (with one leftover. We'll say they are Green Party, just as a joke), and then 1/5 of each of these strongly opinionated groups feels it is OK to lynch congress. From each group, that is a bit over 6 people. taken in isolation, 6 people out of 100 is small change. However, when you add all three groups together, since all 3 groups have that same demographic, you end up with nearly 20 people, which is close to the magic number to reach the tipping point.
They dont need to agree on who to lynch, only that lynching is acceptable.