Liberal vs Conservative

Liberal - Favoring proposals for reform, open to new ideas for progress, and tolerant of the ideas and behavior of others; broad-minded.
Conservative - Favoring traditional views and values; tending to oppose change.

You have 3 addition obvious groups:
Further Left - Radical Liberals, which include socialists, communists, anarchists. They might be 10-15% of the country.

Further Right - Radical Conservatives, which include, tea party nuts and randists

The Middle - Centrists 

If you split the groups into 5 equal parts of 20% each, you will always get 60% in the middle, center-left, center and center-right. Whoever wins The Middle will pretty much always win the general election. They have the numbers. Even in primaries, the candidate which is closer to the center tends to win. (look at gore, kerry, mccain and romney, all of them were centrists to some degree or another compared to their competition. 

A third party? LOL
The far right would be too small, the far left would be too small, and these are the people who WANT a 3rd party, which would really be a 3rd and 4th party.

The only 3rd party that could work at all would be a centrist party (which is what the democrats have become - clinton and obama are both centrists or even slightly right of center.)

A centrist party could be from 40-60% of the voters, with 20 to 30% being on each side.

The centrist party would almost always win.

IF the GOP splits in two parts, they will always lose to the democrats. If the DEMS split, they will always lose to the GOP. Therefore, neither party will every split.

It would be interesting if center-right members left to become centrist-independents and caucused with the democrats. Shifting the majority further toward the center to center-left. The likelihood of the reverse happening is lower, that shift has already happened over the last 50 years with conservative dems switching to the GOP.