Twitter deprecated Twitter API v.1. So this info is also deprecated now. You can access the same api by using the URL https://api.twitter.com/1.1/search/tweets.json. Though this endpoint does not seem to be identical to the previous endpoint outlined before.
As far as I know Twitter Search API is the best thing we've got as of now. And Twitter Search API supports searching timeline of any user. In fact "Search" text box of Twitter (at the top of Twitter page) uses the search API, so you can experiment using that search box.
For example searching
twitter from:yourusername
shows your tweets with word twitter .
You can use the same query for searching from your timeline, or from any users timeline. An API call identical to the example query would be
Your home timeline, the page you see when you log in, will contain tweets from your own account along with all of those you are following and other tweets that have been retweeted (if you haven't turned that off).
When you view a profile's timeline you only see tweets from them and their retweets. You'll know you're on a profile timeline when the URL is like:
https://twitter.com/{username}
How they keep up depends on how they use it and various apps they might use with Twitter.
Some people follow thousands but don't really check their timeline and only look at any mentions toward them. Others might create a list or two with a few tweeters and only check that, cutting down on the noise.
Best Answer
search string min_retweets:2 OR min_favs:2
And then, choose search filter "people you follow".