Though I don't think we've had a West Wing remake, and it's a different genre, I wonder if WW had any influence, stylistic or otherwise, on The Thick Of It? (which I believe has been adapted or remade for US?)
Re: New Tricks US - how about Olmos and McDonnell (right ages). I'd watch that.
West Wing: sort of, but on radio (Radio 4) - Number 10, with Anthony Sher and Damien Lewis as the two Prime Ministers it's had so far over five seasons. Also, there's been some TV series which are like The West Wing as originally pitched, with the focus on the President's staff, such as Party Animals.
As for New Tricks: it's amazing that nobody in the States seems to realise the retired could be a huge market (mind you, nobody in the UK expected New Tricks to do as brilliantly as it has). Just hire the main quartet from iconic 80s cop stars (how about Harvey Keitel, Tom Selleck, Daniel J Travanti and... oh, Kathleen Turner, and watch it top the ratings...