Obviously our two-party system is "strong" enough to prevent it from happening now. But given the fact that in the hypothetical hung parliament scenario, you would need a coalition congress not only to elect a speaker, but the same coalition for every committee and for pretty much all procedural purposes. This seems like such a mess that I can't imagine it ever working.
So my question is: has such a situation (no majority party in one or both houses of congress) ever happened in US history and how was it handled?
Not that long ago there was an even 50-50 split in the U.S. Senate (107th congress).
They came to a "power sharing" agreement on leadership, committee budgets, etc.
Initially the Democrats were the "majority" party (because Gore was VP), and then the Republicans were (because Cheney became VP).
Midway through the term Jim Jeffords (R-VT) decided to caucus with the Democrats (essentially leaving the Republican party), and the chamber was reorganized with the Democrats in the majority. At this time the "Power Sharing" arrangement was discarded as well.