Yes, it's kind of a crazy phenomenon. It was basically where US and even other western liberals put their fantasies of what a 'real president' looks like during the W Bush administration. Since so much of their engagement with politics is just entertainment the west wing was a satisfying replacement for them- so while the US was committing war crimes across the globe they got to watch a show which told them comforting lies like the 'conflict in the middle east' is because of Issac and Ishmael (but it could still be solved at Camp David), or that if you just sit down with a conservative and have a beer with them you will reach a reasonable compromise.

While it had the veneer of being progressive it was incredibly regressive: anti-feminist, anti-protest, pro-NATO, and extremely Islamophobic just to name things off the top of my head. Its fantasies were also cartoonish: the final season of the show featured an election and the Republican nominee is a pro-abortion advocate from California while the Democrat winner is an anti-abortion Catholic, young, charismatic Latino- who makes the republican his secretary of state. The young charismatic guy winning the election in the show was deemed prophetic of Obama's win 2/3 years later by many fans

When the creator of Veep got a tour of the white house from Obama's press people they described their jobs and various rooms in the white house based off of the west wing's characters and which rooms had important scenes happen in them. For example, they described the Roosevelt Room as the room where the fictional president watched a fictional bombing of a fictional version of Iraq instead of describing it as the room where national security council meetings have happened for the previous 50 years.