“How, exactly, is he going to do that?”
The House passes a bill to repeal the 87,000 agents. Likely he can get the entire Republican caucus in the House to vote for this so assume it passes the House. It then goes to the Senate. Schumer’s Democrats will likely vote it down, joined by a few Republicans (Collins, Murkowski, possibly Romney). It dies in the Senate, McCarthy can say he tried.
Even if for some reason a few Democrat Senators voted with Republicans to pass the legislation in the Senate, Biden will almost certainly veto the legislation.
Essentially repealing the 87,000 IRS agents is an empty promise. It lets McCarthy appear to be doing something positive for the GOP voter base and it allows the Democrats to preserve the status quo.
If McCarthy uses the Holman Rule and GOP solidarity is maintained, they can reduce the funding for the 87,000 IRS agents down to a point where it only exists on paper.
Only the House is involved.
Or they can attach it to some bill that the Senate cannot vote down, and Biden can’t veto.
It was an empty promise, from McCarthy, before the proposed rule changes. See my post just above yours for how things were changed by Gaetz and crew.