TLDR: Kamala can control the Senate even if Mitch remains majority leader
The Vice President is in a constitutional gray area; nowhere in the document does it say whether the Vice President is part of the executive or legislative branch. All it says is that they are the “president of the Senate,” which would imply the legislative, but most VPs are given executive authority via statute and precedent. In practice, the Vice President does very little in their role as president of the Senate; the constitution gives them the authority to preside over its sessions (the president presides, makes sense so far), but that power is often deferred to the President pro tempore of the Senate, which can be thought of as the vice president of the senate; when the Vice President is unavailable, the constitution gives the president pro tempore the authority to preside over senate sessions. In practice, neither the vice president nor president pro tempore do much presiding. The president pro tempore, although third in line for the presidency, is a ceremonial job given to the longest serving member of the majority party (which usually means they’re the OLDEST member, putting an 80 or 90 year old dinosaur just 3 heartbeats away from the nuclear codes). In practice, the Senate picks its own presiding officer, rotating through a number of junior senators to give them some experience. This is all just set up for my point.
The Senate writes its own rules of operation, called the Standing Rules, of which there are 44. None of them actually give any power to the senate majority leader. Their power derives from attitude and respect for precedent, not actual statute or law. Technically no senator is more powerful than any other, and any may speak and bring legislation to the floor for debate, but the majority leader has co-opted this power all for themselves because 100 years ago a presiding officer decided that party leaders should have seniority when it comes to speaking. The rules before this were that the presiding officer had to pick whoever stood up first, so if two people stood up at once it was up to the presiding officer to choose who got to speak; the seniority precedent said that if the senate majority leader stands, they get the floor no matter what. But this isn’t part of the rules! This isn’t written down anywhere in the constitution, and the Senate never voted to make it statutory!
The Vice President could decide to undo the precedent set all those decades ago, and set NEW precedent, allowing them to pick whoever stood up first again, OR giving seniority not to the leader of the majority party but to the leader of the Vice President’s party instead. The Vice President is constitutionally allowed to preside over every senate session, so they could decide that, in their role as president of the senate, their party gets to be senior over the other party, regardless of how many votes they have. This would stop the majority leader from holding legislation hostage by allowing anyone within the VP’s party to propose legislation, which could then be voted up or down by the full senate. Whether the legislation passes is up to the American people electing their senators, not the senate majority leader. If the Democrats don’t win both Georgia senate seats, they could still open up the floor for votes, and with moderates like Romney and Collins who would vote how they feel instead of voting for how McConnell wants them to, the Democrats could have a chance of getting their agenda passed with a slim majority vote.
This would be seen as a partisan power grab, but then how is that any different to McConnell’s modus operandi? This would prevent him from holding Supreme Court justices hostage (though it’s not a guarantee that any given justice would be confirmed, just that they would get a vote), this would prevent him from holding cabinet secretaries hostage as he has threatened to do.
Joe Biden chose not to use this power when he was Vice President because he didn’t want to step on any toes, make any enemies, or defy and precedents. Kamala Harris though has stated that being a senator under McConnell’s “leadership” is boring because they don’t DO anything, so she might have the audacity to shake things up. The Democrats have options, they just need to learn to play hardball. If it’s not illegal, then it’s legal; that’s the Republican motto, and the Democrats need to start playing by those same rules!