Nope. At livable temperatures, water is compressible by 0.000053%. Even at 150 atmospheres (2200psi), water compresses less than 1%.
For the mathematically addicted, visit here for a decent, clear explanation:
http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html. Compressibility does not become important with large volumes of water at most pressures. That is how the fire dept can pump water out of hoses at very high pressures to reach the upper floors of buildings--they apply pressure to the water and instead of compressing, it moves. Water can be squirted much farther than air, which is very compressible.