I'm not convinced. The differences between the US and UK system aren't that big;
It's a matter of degrees.
The primary difference is that the UK parliament is elected by a single constituency (the whole of the UK) following a first-past-the-post system. This means that yes, there may be two major parties that get most of the available seats, but if a concerted effort is made by a third party to focus all their votes on a single person, that person has a reasonable chance to get into and influence parliament.
In the US this is very, very different. Congress is strictly regional, with 50 constituencies voting on a limited number of seats for each constituency. Further, within each state each seat is regional. So I can only vote for the senator and representative for my region - I can't vote on all the available seats in my state, I can only vote for one. This may vary by state, and I suspect that I do get to vote for both senators, but I only get to vote for one representative even though michigan has several seats in the house of representatives.
Therefore if a third party wants to get a candidate into the house of representatives or the senate, the third party has to convince a majority of the people in a region to vote third party - which simply isn't going to happen, especially since the regions are drawn by the ruling parties.
So this one difference seems very large to me, and explains why third parties have little to no chance to participate effectively in the US election process.
What happens instead is that they gain support within one of the two parties that are leading, and then try to change the party, or at least get their candidates a seat and then try to push from there. This is one of the reasons the democrats and republicans sometimes seem to be all over the place. The tea party, by all rights, is different enough to be considered separately from the republicans, but they know they won't get anything if they don't work within the two party system, which means "corrupting" the republicans.
By some measures, Obama isn't a democrat, and Romney isn't a republican. But they aren't going to go anywhere if they don't work within the two party system.
The states are not going to release their seats in congress, which is what would be necessary to make it so smaller parties have a chance of getting a seat in congress.
So the two party system controls politics, and will continue to do so in the foreseeable future. Changing the voting method to a run-off or any other method means nothing if the states won't give up the electoral college (which mirrors the seats in congress) or their seats in congress.