Sure about that? Mayorkas can be impeached merely for suggesting “the border is secure” several times.

How is that a "high crime or misdemeanor"?

At any rate there will be no shortage of GOP votes. They will also have some border state democrats.

The GOP only has a two-vote majority for the rest of the term. They will have "no shortage" of GOP votes, but they need to get virtually all of them to impeach. At least a handful will likely vote against it, because there simply is no hint of criminality on Mayorkas' part.

Every cabinet official exercises the discretion afforded by their office in terms of priorities and policies in the manner directed by the President, not Congress. Every Congress has disagreements with the Executive all the time in how the Executive is allocating resources and setting priorities in the various departments. That's why impeachment isn't available for claims of maladministration, claims that the official is doing a terrible job (as opposed to actual criminality). The President gets to decide, through his cabinet officials, how the laws will be executed - and if Congress doesn't like it, the Constitution doesn't provide for them to just start throwing out cabinet officials. There will be a number of Republicans who will have concerns about whether Mayorkas has done anything that is impeachable, no matter how bad they think the Administration is mishandling border policy.