It appears that my site pulls in more than 2000 articles in just a couple of days. Is it possible to increase this amount? By doing so, will this slow down the site. It appears it may, but not sure.

Yes.
In admin/modules/ folder open multiheadlines.php file.

Look after this line [392]:

And change 2000 with your desired value. (But be aware, 50 must divide the new value exactly).
After go to your Multiheadlines admin panel
->General Settings->Empty DB when reaches:
and set there a higher value.


Yes a little bit, depending on new value. When there are many more entries in database the queries in database will last a little longer[but this is acceptable]