Why does windsheld washer not work? Could it be that the tubing is clogged?

I would not use anything more than say 10psi of pressure. I doubt using air pressure will fix the clog if that is the problem, because the pump uses 10-20 psi in normal use. You may have to disconnect the nozzles and use a pin to clean out the ports or find the clog in the main line.

Do you hear the pump working like it's trying to work? If so, then it is likely that your washer nozzles are clogged or the tubes to the washer nozzles are clogged. Try: http://www.videojug.com/film/how-to-clean-windscreen-washer-jets

and:
http://forums.audiworld.com/showthread.php?t=30886

{: ) The rear washer pump is attached to the washer fluid reservoir. Below the left headlamp assembly. Ignition on, engine off. Switch ON the rear washer control. If you can hear the rear washer motor works, check for clogged hoses and tubes. If it's not clogged, your motor could only be running but not pumping.
If you cant hear the washer motor at work, its probably faulty.
To rule out if its a control switching issue, get a test light to check for voltage at the washer connector if you could only access it. Its better to check on that end. If you cant access it, at least probe the rear washer fuse at the underhood fuseblock. The test lamp should light everytime you switch on the rear washer switch.

Check to ensure the front reservoir pump is connected and receiving power. Is the fuse bad?
It is possible the pump inlet is clogged. This would require removing the reservoir and flushing it.
If this is a washer with an external, self-priming pump, is the pump uptake tube in the cap missing?

Either the tube leading from the pump in the front is clogged or iced up, or the tubing has becoming disconnected.

It's also possible that the motor is spinning for the pump, but the impeller is not spinning with it.
But, I would check out the tubing from the windshield spray area down to the reservoir.

A crack in the tubing, clogged up sprayers on the hood. Check for leaks while a buddy activates the pump. Try cleaning the sprayers with compressed air. Listen to the pump, do you hear it working? If not, you have a bad pump or no power.

Check for airlock on pump input (if pump not mounted below water tank level),
check water delivery at pump outup port is ok,
check for kinked/crushed delivery hose,
check for blocked squirter nozzles.

Hi and welcome to FixYa,

Initially, your concern could be caused by:

• clogged hose/tubing from washer pump to nozzle;
• clogged nozzle;
• faulty spray pump (inside the washer bottle);
• faulty switch;
• faulty connector/wiring.

In most cases, it would be clogged nozzle or blocked hose/tubing.

Good luck and Thank you for using FixYa.

You didn't mention any lost fluids so we can assume that no hapless mechanic has accidentally pulled any tubing loose from the supply. 
If, as in many cars, the path of the tubing connecting the washer fluid bottle to the jets on the cowl are visible, carefully pull one the tubes loose and have someone operate the washer to see if the pump is doing anything any more. You may be able to find the 'Y' junction where the tubes split off to feed the two jets.
The rear window washer has its own fluid supply and pump so is completely independent of the front.
If you find the pump working, then you will have to carefully poke a soft, small gauge wire, preferably copper, to try to clean the jets themselves. You probably have some small bits of something clogging the jets and it can help if someone is keeping the washer pump running while you try to clear them as the pressure will aid you.     
Worst case, the jets can often be replaced fairly easy and at a cost of a few dollars. 

Try removing the plastic panel underneath/forward of the RH wheel arch, the washer bottle is there, remove the pump by pulling straight out of the bottle. There is a plug and two hoses connected to the pump. You will probably find the mesh filter is clogged, clean and try it. Some washer pumps have a valve on the side where the hoses connect, do not try to dismantle this,