There have been tons of posts regarding 870's and Winchester el cheapo ammo.
My 870's are all well worn and have thousands of rounds through them, so I haven't seen it. I was skeptical until a friend of mine showed it to me. I fired 2 rounds of the Winchester stuff, and had very hard extraction. I then fired several rounds of Remington and the gun cycled perfectly.
Do a search, you will find a lot of posts reporting the same. It appears to be an issue of the ammo and Remington Express tighter and less finely finished chambers. Lots of folks have reported that they corrected it with a chamber polish job.
With that said, I use the cheap Winchester stuff in my Beretta's all the time, and have never had an issue with it.