I can't find any. It's kinda ridiculous.

Diawa Lexa 300.

Best reel for cheap.  How cheap is cheap?  Freshwater or saltwater?

 

A Pflueger President 40-size will hold about 120 yards of 20lb mono for $60.  Can't say if there would be any line management issues on that size spool however.

 

There's a bunch of fairly inexpensive spinning reels intended for saltwater inshore fishing that will hold plenty of 20lb - some as low as $40.  Check out the saltwater spinning reel section on the BPS web site to get some ideas...

I agree, it's ridiculous.

 

Try braid.

Any Spinning Reel can hold a good amount of 20lb braid. 20lb mono, copoly, fluorocarbon... no bass spinnining reel will do the job that well IMO. With those lines of that size you should be using a baitcaster.

Almost any spinning reel can hold Fireline 20# braid. It's the diameter of somewhere between 8 & 6# mono. I have it on a Pfleuger Trion as well as an old BPS Viper spinning combo right now. I've been using it almost all of 2015 with nary a knot on either reel. Trion's a $40 reel. It's the best bargain I've found in bass fishing in many a year. I'd say its quality is on par with reels $20-$30 more, but it isn't made with lightweight materials. Don't get the 40 size unless you just want to. It's a tad heavy. But the big spool casts very well and the drag is super-smooth. I've whipped a couple bigger bass with it.