For that matter, most countries are smaller than the US, both in size and population. There are only two countries with a larger population. China has one ruling political party, and India has had prime ministers from many different parties.
For a full accounting, look back to the rise of the two party system during the Jacksonian era, or the current system of Democrats and Republicans (replacing the Whig party) started in the 1850s.
An explanation based on population size would have to be able to explain why it is that the current two party system in the US started when it was a much smaller country.
The US population in 1860 was 31,443,321. There are now 42 countries with a population larger than that.
