The US political classes might feel a bit aggrieved at parliaments decision over action in Syria, but it will not substantively effect US-UK relations, as some commentators - and some UK politicians who were quite hawk-like in their desire for military intervention have been suggesting.
The appetite for military action by the US in Syria is not great amongst the US public, as best as I can tell, and Congress are already muttering that they wish they had the same ability to debate the issue and hold the executive to account as we do here following the vote in Parliament last night.