I broke my brass cleaning rod yesterday (yes, after researching I now know that brass is terrible anyway) so I went to Dunham's to get a new cleaning rod. I looked around at found this little 1 piece cleaning rod for much cheaper than the rest:

http://www.tetraproducts.com/product_view.asp?ID=50

From looking at it and feeling it, I thought it was the type of carbon fiber or nylon rod that the other popular cleaning rods are made from. After looking at their website, I found out it is made of blued carbon steel. Will using this type of rod have any negative effects on my rifles?

Thanks

Only if you try to pull it out crooked. I mainly just use a boresnake, if not I use a good ol G.I. Rod. If used correctly none of them will damage your bore.

Why is brass terrible?

The only difference between a quality polished stainless steel one piece rod and a one piece carbon steel rod is that the carbon steel rod can rust more easily when the finish rubs off.
Other then that, many older, especially USGI steel rods were rougher finished.

Brass and aluminum rods can be bad because they're softer then steel.
Grit can embed into the soft metal and that can turn a rod into an abrasive lapping rod that can wear the muzzle quickly.
This is counterintuitive.  You'd think a hard steel rod would be more damaging, but a polished stainless rod is actually easier on the barrel IF properly used.
Also the softer rods bend and flex more.

If you allow a bare aluminum rod to sit unused, over time it will get a crusty white coating.
This is aluminum oxide, which is what grinding stones are made of.  This can really damage a bore fast.
At least this is what a metallurgist told me.

Bottom line is, you're only going to need to buy one rod of a certain size in a life time.  Unless you damage it it will last a life time, so you might as well buy a quality stainless steel or carbon fiber rod to start with.