What do you think they meant by "no factions?"
I'm one of those controversial people who say I wish my country would get over the Founding Fathers (or failing that, perhaps even call them "The Founders," as fathering had nothing to do with it). This awe sometimes turns my stomach. Read Howard Zinn's A People's History of the United States, and Thaddeus Russell's A Renegade History of the United States and you come out with a better idea of what the Founders were about.
It's the Founders design failure that saddles us with two parties. Other countries see the their legislature as sort of interface between parties and government. Our Constitution doesn't even deal with parties, because the Founders thought we could do without them. To be accurate, they wanted to establish a one-party state where the government was the party, and the party was all made up of rich, privileged white men. For the ones who actually wrote the Constitution, historically, there's no doubt about this.
However, they failed, and they way they failed ensures that the Congress isn't set up to work with parties. So, the system can sustain only two. Basically, the conservative establishment party (Republicans) and most other people (Democrats).
The only time this country has sustained more than two parties, has been either fleetingly for one election, or when one of the two parties is dying (the Whigs). However, in fact, for a fairly long period, between 1820 and 1850, there was really only one party. And the period was known for its extension of slavery, and conquest of the Indians and war with Mexico.
Meanwhile, a one party state is associated with totalitarianism. So, please don't quote people who quote the Founders with awe about what they predicted. They weren't prophets.