Major news sources will always get more overall exposure simply through quantity because they publish so many articles every single day. However, low traffic sites and blogs will get their content promoted at or near the top of the search results when it is indexed in the same manner that the high traffic sites do.
I understand there are sites you dislike which is why I added an Upgrade global filter feature where you can block sites, topics, keywords, etc. that you do not want to see. Other Upgraded users can do the same when they do not want to see content they dislike as well.
The Popular search results are currently supplemented by a variety of hand-picked source feeds because the site is new and there is not yet enough traffic history to generate an accurate list of popular content, but that will change once more people start using the site.
Of course people will not be happy with some of the sites selected if the target site has a political bias that they disagree with, but it is only temporary until traffic starts to grow more on the site.
I already have it built into the engine to ignore the supplemental sources once the activity level hits a certain level.
That said, it will still come down to the users. If a lot of users are viewing specific content, it will likely find its way to the home page.
On a side note, you can change your default home page via the Settings page to avoid the popular search results.