The basic US position is that outlined in the 1993 Oslo accords:
Israel should withdraw militarily from the Gaza Strip and the West Bank (excluding Jerusalem.) An interim Palestinian authority should be set up, and negotiations towards a two-state solution should proceed over a five year period, ending in 1998.
Thus the recognition of an independent Palestine State was dependent on the success of the negotiations between 1993 and 1998. However these stalled. Israel failed to withdraw in full. The people rose up in the second intifada. The interim Palestinian Authority became a permanent government in the part of the West Bank that Israel had withdrawn from, while Hamas took control of Gaza. Israel has effective control of most of the West Bank. US recognition of a Palestinian state is dependent on a peace process that leads to Israeli recognition of a Palestinian state, and right now that looks very very unlikely in the short to medium term.
So the US would support a two-state solution, if one can be agreed upon. But that depends on Israel and the Palestinians.