Politicians from McCarthy period at resort, leaving hotel (10,5)

I believe the answer is:

democratic party

I'm a little stuck... Click here to teach me more about this clue!

'politicians' is the definition.

'mccarthy period at resort leaving hotel' is the wordplay.
I cannot really see how this works, but
'at' is within the answer.
This explanation may well be incorrect...

'from' is the link.

Can you help me to learn more?

(Another definition for democratic party that I've seen is " Republican's opponents?".)

I've seen this clue in The Times.

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