There is no such "favoring" anywhere in the Constitution. We have multiple parties and, in fact, one of them was — the Whigs — once strong enough to gain major chunks in Congress and the Presidency.
Uh, have you read the 12th Amendment? I quote the first relevant section, "...if such number [of electoral votes] be a majority of the whole number of Electors appointed..." by definition forcing it to mean 50.0000001% or greater (AKA a majority). So, if 3 candidates are in the running, one gets 10%, one gets 45% and the other gets 45%, no one wins. Following that scenario, "...the House of Representatives shall choose immediately, by ballot, the President..." means that, whoever has the majority most members in the OUTGOING House, will (almost undoubtedly) have the winner. Therefore, we would have to magically elect at least a reasonable percent of third parties to have even a REMOTE chance of a third party mattering. Frankly, the 12th is one of (if not) the worst amendments created, not only permitting the focusing of parties, but downright endorsing it.
What confuses many people — including, it seems, yourself — is that in the US we do not vote for parties. We vote for individuals. The individuals may or may not choose to affiliate with a particular party, but such affiliations are not binding. An elected lawmaker can quit/join any party without any official consequences to his position.
I'd thank you to not put words into my mouth, nor attempt to extract thoughts from my mind. I have not voted for a party, ever, in my life. I have always voted for whomever I felt had the most reasoned decisions, the most education, and the most experience as to whatever posting they were applying for.