Why does my new bike's back wheel not spin easily?

First thing to do is check your oil levels. I'm not sure if that bike uses a separate transmission oil. Low oil can cause strange noises when in gear.
Can you be more specific about the noise? Is it a metal against metal sound? Is it a rattle or a smooth noise? Does it disappear between gear changes, when you pull in the clutch?
Check the easy stuff first. You don't need tools fo these checks. If it has a centre stand raise it onto that. Get a helper to gently put some weight on the back of the bike to raise the front wheel off the ground. Spin the front wheel by hand and listen. You should only be able to hear a very quiet gritty noise from the front brake. Spin the front wheel a bit faster and check it's spinning straight and true.
Get your helper to move to the front of the bike to raise the rear wheel off the ground. Put the bike in neutral, spin the rear wheel and listen. There should be two different, quiet noises. A gritty one like the front wheel and a quiet rattle as the chain moves through the rear wheel sprocket and transmission sprocket. Put the bike in gear and pull in the clutch so the wheel will turn. Spin the wheel again and listen to see if the noises change. Lastly spin the wheel faster and check it's lined up and spinning straight and true.
Use the comment button below and i'll see if I can help you more.

Hi James:
If New, I'd take it back to the dealer.
If used.....
Set bike on jack so front wheel is raised. Make sure it is secure so can't fall.
1) Remove front brake pads........... spin wheel If it still squeaks, remove wheel and service bearings.
If no squeak when brakes removed, service brakes.

Starter clutch is behind the alternator rotor. It should turn only one way. If it is bad (you'll have to take it out to see) it will turn either way.

ONE AT A TIME, loosen the nuts securing the training wheels to the rear axle and slide each one upward a little bit so it float a little bit off the ground when the bike is vertical, then retighten the nut.

As she develops her handling and balance skills she'll need less help from the training wheel. So you can gradually raise them a bit higher as she masters balance and then she'll develop the 'lean' for turning. Ultimately, you remove them entirely.

I hope she's wearing a properly-fitted helmet.

http://www.nhtsa.gov/people/injury/pedbimot/bike/easystepsweb/index.htm

The set screws in the center of the axle are there to keep the axle centered in the frame. Only the right wheel is powered which also means only the right wheel brakes when operating the rear brake. This is because the rear wheels must be able to spin independently when turning because the outside wheel will move faster. Unfortunately no one builds differentials at this price.

If you have wheel wobble you need to determine if the axle is bent or the wheel is not true. Prop up the rear of the bike on a stand and remove the problematic wheel. Manually pedal the bike and check the axle as it spins. If the axle is wobbling then it is bent and will need to be replaced. If it spins true then the wheel is the culprit.

The axle is relatively inexpensive and can be ordered through a Schwinn dealer. Any bike shop should be able to true a wheel for around $15-$20.

It sounds like you have a piston that is not fully returned and is sticking.

Get a big flat bladed screw driver, take the wheel out and very carefully insert the screw driver into where the disc would sit and use the screw driver to try and push each brake pad back in without damaging your brake pads.

If this works go to a local bike shop and ask them for a avid brake insert for transporting your bike so this does not happen in future! :)

You may have a locked up wheel bearing or you may have an object stuck in the chain. Can you spin rear wheel by hand? If not, most like bearings, if so, then you may have bent gear tooth or something stuck in chain. Check derailer to make sure it is not bent

Losen the screw

The bikes are pre-assembled by a machine that overtightens the rear axle.  I had the same problem with my daugher's 12 inch huffy princess bike and my other duaghter's 16 inch Schwinn bike.  If you loosen the nuts on the back axle it fixes the problem.  I have read that the idea thing for these bike is to have them re-assembled and re-lubricated by a bike shop, but I thought this might cost as much as I paid for the bike.