Even if the House still is controlled by the GOP after this November’s elections (which is the likeliest scenario), you must remember that when there is a contingent presidential election (one in which the House has to choose from among the three top finishers in electoral votes), the House votes by state delegation (with California, Texas, Vermont and Wyoming each getting one vote), and it takes 26 state delegations to elect a president. So if the GOP holds on to the House but only has a majority in, say, 25 state delegations (with the Dems controlling 23 and 2 being evenly split between the two parties, then the GOP Representatives would not be able to elect the Republican as president. You also have to consider the fact that there likely would be a third candidate apart from the R and D nominees (unless the R and D candidates tied at 269, or else neither one got to 270 because of abstentions). In other words, it’s more complicated than just which party controls the House.
And this law would apply if one of the presidential candidates among whom the House would be deciding dies after the Electoral College has met. Even if the GOP controls 26+ state delegations in the House, if the GOP nominee is dead then the GOP House either would (i) elect the dead man (in which case the VP would become president on January 20, and if no VP candidate got 270 EVs then the Senate—perhaps controlled by the Democrats—would elect the VP-cum-President) or (ii) be forced to elect the Democrat or the third-party candidate that received EVs because one of the houses of Congress (*cough* the Senate *cough cough*) refused to count EVs cast for the dead Republican pursuant to the 1872 precedent involving the death of Horace Greeley. By adopting the proposed law, it would permit the GOP House to elect a Republican president if the GOP presidential nominee is dead (either the dead man’s runningmate, or else a replacement candidate selected by the dead Republican’s presidential electors in a revote); without the law, it would not be able to elect a Republican.
I already knew that, if the House votes for president, each state gets one vote. I hope that all Americans know that.