> why would they say that and then continue to run for elections?
Are you suggesting that the USA should have a single political party? Anyone that cares for democracy would be against that, regardless of their other political views.
My guess would be what they meant was that they should quit. Ie either you respect the intelligence/morallity of the people who you want to vote for you, or maybe you shouldn't be trying to represent them.
And not quit as in leave only a single party, but quit as in leave a vacuum for another party/candidate/etc to step in.
Note these aren't necessarily my personal views, just trying to help clarify what I believe the commentator meant.