IMO it is the presidential system, more than first-past-the-post, that accounts for the weakness of third parries in America. After all, FPTP has not prevented sometimes substantial third parties from developing in the UK or Canada. Voters do not want to "waste" their vote for president, and while it is true that a third party could theoretically influence the result of a close election by getting a few electors and then bargaining either in the Electoral College itself or in Congress, such bargaining has widely been considered illegitimate, at least since the "corrupt bargain" of 1824-5.
And this fact affects the third party vote not only for the presidency but also for Congress, etc. Americans generally do not take a political party seriously--even in elections for Congress or for state offices--unless it can seriously compete for the presidency. (After all, in the UK or Canada, even if a party has only a few members of Parliament, these members can, in a hung Parliament, help decide who forms the Government. They have no such power in the US, unless the election goes into Congress, which most people consider a result they want to avoid.)
And of course another reason for the lack of a third party is that the two major parties *are* significantly different ideologically, even if not as much as some people wish they would be. If both major parties were ideologically almost indistinguishable, there would be--despite the presidential nature of American elections, and despite the FPTP electoral system for Congress--many more third party votes than there are now. Some evidence of this is that in fact there *was* considerable third-party voting in the US before the New Deal (and no doubt there would have been more if not for the special case created in the South by the racial situation). See
http://economics.mit.edu/files/1224 "Over the period 1890 to 1920, third party candidates for the U.S. House, Governor, and U.S. Senator won more than 10% of the total vote in 16 states.3 In contrast, over the period 1940 to 1970, third party candidates for these three offices never won 10% of the total vote in any state. More than five times as many third party congressmen were elected to the U.S.House in the period1890 to 1920 as compared to the period 1940 to 1970.4 Furthermore, in state legislatures third parties won a plurality of seats in either the upper or lower chamber of nine state legislatures during the first period (1890-1920), compared with none during the second period (1940-1970)."