Do you think it is likely a new political party will emerge in the United States either as a centrist party (because the Republicans have lurched so far right in recent decades) or a left wing party (because the Democrats have lurched to the centre)?

The structure of the electoral system makes this impossible. There is already great variation in the state and local parties' positions, but for presidential politics, they have to be part of a coalition that can win states nationwide.

It is not likely. Moderates are by nature not activists. They're not angry enough. You need activists to build a party. If moderates were activists, the GOP would have withstood the Tea Party better. The Tea Party grew and won primaries because the fringes are more motivated. A far left party would lose too many statewide elections. Not a good choice for ambitious politicians. In fact there are far left parties and they never win anything. Without proportional representation, you have to win elections outright to get any power. No power, no money, no voice. That makes it very hard to attract good candidates or maintain activist and donor commitment over the time it would take to grow into a party that could start winning. It would be hard to peel off support from existing parties. Carving a third party out of an existing party when the two are so evenly matched would just ensure victory for the party that didn't get carved. The lesson of Bush/Gore/Nader will not soon be forgotten. Most will be willing to compromise in their own party in order to beat the historic ideological enemy.

http://en.wikipedia.org/wiki/Duverger%27s_law suggests that any first past the post election system would eventually work its way down to two parties.  He also lists counter examples like Canada where there are three national parties (From the left NDP, Liberals and Conservatives), one fringe party (the Greens) and one regional party (Bloc Quebecois).  The reason that the third and fourth party grew and became stronger is that they  were originally a regional party.  The NDP started on the prairies in Western Canada - mostly in Saskatchewan and eventually grew from there.  The Bloc is a separatist party that never had the message to grow beyond Quebec and is slowly dying out.  Based on his theory it sounds like if an American third party were to rise, they should focus on a territory (California, the Deep South or New England) and build outward from there.  They would have to have a message that will first grab people in their first area but the message would have to be transferable to other areas.  It would have to grow organically and not try to start everywhere at once.

The other posters point out the high entry barrier to a third party. It's improbable, but not impossible. One scenario. The Republican mainstream jettisons the Tea Party, and enraged members of that faction, financed by oil money, form a separate Tea Party. It could even be viable, in a sense, if the Teapartiers are astute enough to sell their votes and services to the highest bidder among the conventional political groups. Now, that's an innovative idea -- a party for hire, a mercenary party.

The only scenario where I foresee a new political party forming requires the GOP far-right preventing the party from moderating over the course of the next decade. In this scenario, the influx of former GOP moderates and big business donors into the Democratic Party, splits the Dems over time and brews a progressive party. Three parties would not exist for very long though. Either the Democrats would become the new conservatives (Although nowhere near the right today) against a Progressive Party or the GOP base relents and moderates, allowing the Democrats to cater back the left. Donald Trump is the wildcard to this. He'll either accelerate this theory (Driving big business to the Democrats) or destroy it (Drawing previously untapped voters into the electorate and lengthening the GOP's national relevance).

If you think the Republicans moved right, and the Democrats moved to the center, I'm not sure you have the balanced frame of reference required to debate this question.

As an outsider looking in I can't tell whether change is at all likely. Never mind about what that change might be. I think something ought to happen because the poor in the US are effectively disenfranchised. No "candidate of the poor" could raise the money to stand. Worse than that, right wing propaganda appears so effective that many poor people vote against their own interests. At least the status quo has saved the US from a truly socialist government which would wreck the economy for years to come.

Both the Republicans and the Democrats have lurched to the left.