From the Twitter Help Center, for aspiring politicians:
"What happens to Tweets I delete? - When you delete a Tweet, it is removed from your account, the timeline of any accounts you follow, and also Twitter search results.
- Retweets of the deleted Tweet will also be deleted.
- If other users have quoted your Tweet (i.e. copied and pasted part or all of your text into their own Tweet) their Tweets will not be removed.
- If other users have Retweeted your Tweet with a comment of their own, their Tweets will not be removed.
- Tweets may be cached or cross-posted on third-party websites, applications, or search engines. We cannot remove Tweets that are not on Twitter."