The issue under discussion is the Organizing Resolution, which details the rules, membership, and budgets of committees, among other things. The Organizing Resolution is a "simple resolution" which technically requires only a bare majority to pass, which the Democrats possess thanks to the Vice President's tie-breaking vote. The reason Senator Schumer is discussing a power-sharing agreement with Senator McConnell, besides fairness and the fact that this is how it's been done before, is that simple resolutions can be filibustered, which means that 60 votes are required in practice to pass the Organizing Resolution.
If Senators McConnell and Schumer can't come to an agreement, there are only 3 possible options:
- Continue to operate under the previous Organizing Resolution, which gives Republicans control of committees
- Pursue a backroom deal with 10 Republicans to defy their minority leader and support an Organizing Resolution based on the 2001 bipartisan agreement
- Abolish the filibuster using the so-called "nuclear option" and then pass the Organizing Resolution by simple majority vote.
In an opinion piece in The Week, Ryan Cooper discusses this third possibility:
The obvious solution here would be to call McConnell's bluff and simply get rid of the filibuster now. ... As Akhil Reed Amar argues at length in Duke Law Journal, it is both legal and constitutional for Democrats to invoke Rule 20, which outlines how questions of procedure are adjudicated, to amend the rules and delete the filibuster through a simple majority vote. Then they pass the Organizing Resolution with that same majority.
Most likely, the Senate will come to a compromise on this, that protects the filibuster enough for Senator McConnell, while leaving the door open for it's repeal in the face of Republican obstruction to prevent a Democratic revolt. But if they can't find a compromise, then the nuclear option is really the only way to move forward.