I have a Schwinn floor air pump and its nozzle is the kind you push down and flip up the lever to connect. With a brand new inner tube installed I could not get it to connect with the valve as I have rims with a deep section, with these particular rims even inflated you only have the brass end of the valve showing.
Is there an easy way to inflate the tire with this set up?
The real answer is you need inner tubes with longer valve stems. Tubes come with various length stems to accommodate deep section rims.
There are screw-on valve stem extenders available for both Presta and Schrader that you could use to extend your stems. (I think some Schrader ones are actually for car tires, but they would still work for a bike.)
With out an valve extension, to get started, try pressing down hard on the tire and tube where the valve stem is to press the it out of the rim so you can get the pump nozzle attached. Having someone to help you will make this easier. You can also thread a valve stem nut onto the stem to retain the stem when you try to get the nozzle on.
Another approach to getting started, before getting the second tire bead onto the rim, reach inside the tire, press the valve stem out of the rim, clip on the pump, then fit the second tire bead.
Well, it seems that your pump has both connectors: the car one and the Presta one. (Sorry, I'm not sure about the terminology in English, in Czech they are "auto" and "velo".)
The trick is to get this little gadget which is screwed on top of the valve and then the pump is connected. Now, as the gadget is wider than the valve, it prevents the valve from slipping into the rim. I found it on Amazon under the name Bike Adapter for Air Compressor. However, here even some bike shops sell them. Just be sure you get the correct thing!
One trick I've used for wily valve stems is to use my thumb or a broomstick on the floor or some such object to push the stem as far out of the hole as it will go.
The valve stem may simply not be long enough. Try, as previously suggested above, press on the tread directly opposite the valve in order to push the valve farther through the rim. Hold it in place while connecting the pump. The better solution, again, as mentioned above, is to replace the tube with one having a longer valve stem. If you do this, you may want to consider switching to a tube with a presta valve (you would also need a small adapter for the rim hole, available at bike shop, because the presta valve is smaller in diameter). Presta valves have a nut that tightens against the rim to prevent the valve stem from retreating into the rim.
