This mashup was uttered by Frank Thorp V on MSNBC last Saturday.  It is a conflation of “walk a tightrope” (be in a situation where one must be extremely cautious) and “run the gauntlet” (enduring a series of problems, threats, or criticisms).  “Running” and “walking” might have led to the speaker’s confusion, or perhaps in the end the Democrats really had to run across that tightrope!  A big thanks to Frank King who heard this one and ran it in.