Yes the check is a bit too close. If you move it out where they suggested, it should prime and hold it.
When priming a pump, you really should be able to do it with less than a gallon of drinking water. Just open the largest plug on top of the pump head, and pour the head full.
Then plug in the pump power, and quickly start hand-screwing the plug back in (wrap 2-3 flat wraps of teflon tape of the plug threads cclockwise only as the bottom of the plug faces you). It will bubble air and water (normal), but just keep hand-tightening the plug until it picks up prime.
Once it primes, tighten the plug with a wrench.
If it doesn't prime the first time, just do it again (including new teflon tape) until it does.