its unlikely a third party could win the presidency without winning a decent amount of the congresses. At that point it would be just like any other time when a president does not have a majority in congress. Assuming both the dems and republicans have a good chunk they could likely work with them and get some stuff done. assuming the republicans stick to their stance of just blocking crap they might be able to slow things down and such.

The veto is a strong power. And if the Congress is still staffed with do-nothings, then they can rule by executive fiat like the current administration does.

It's rare for a third party to win more than a single county. Might as well ask what will happen when the seas turn yellow.