Now that I reread that, it says “House shall choose immediately.” Someone might say that the House can consider no other business (especially not a 25th amendment nomination) until that question is decided.
12th Amendment
And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.Terms didn't start on January 20 back then, so the March 4 deadline is interesting. The 20th Amendment addresses this:
20th Amendment Clause 3
If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.This says that the Acting President is only temporary, but Congress can pass a law to fill the temporary vacancy. This is only temporary, as the 20th amendment is superior to any act of Congress, meaning that Congress cannot permanently select an Acting President.
-PJ