There are a few USA third party politic questions out there, but I wanted to focus on any mechanism designed to limit 3rd party influence had a minority gov't setup came to be in the USA. Minority govt's will frequently have the issue of 'being held hostage to minority or special interest groups', meaning that a special interest party can tip the scale between two ruling parties ensuring that their stance is forefront on every issue.
Scenario: For whatever reason, a third party in the USA gains a bit of traction. This can range from a special interest group that fragments from the larger whole (a 'wall' party emerges focused entirely on building the wall between mexico and the US, or a 'public healthcare' party that is entirely focused on creating public healthcare without really having any other defined policy beyond their single scope. A "green" party often fills this role in other nations) or a new centrist party that draws support from undecided and both sides of the aisle. Which ever the case, assume the new setup in both the house and senate are now split so that neither republican nor democrat can form a majority (senate is 48 republican, 48 democrat, and 4 'other'). Ultimately this setup would mean that the Republicans nor Democrats could put through policy without winning over support of this third party, basically allowing the 3rd party to put their spin on any given bill to suit their agenda prior to supporting (the third party here gain tremendous influence for a tiny portion of seats). Of course policy that both republicans and democrats support wouldn't be effected in this scenario.
I do see the ability for independent senators to caucus with the democrats and I'm under the impression minority politics would function similar to that. Are their any particular rules/laws/mechanisms that would address how a minority government within the US?
(no minority politics tag appears to exist?)