150 psi -- good tires for less than $25???
Can't be done, sorry.
A good quality set of 700 X 23 (or especially 700 x 20) are cost you almost twice that on sale.
The high end Michelin's, Continental's, Vittoria's, Schwalbe's and all the rest will be usually $60 per.
If you want a training tire that is "average" and mid range you can get these for $13.95 each. http://www.biketiresdirect.com/pvizf7/vittoria_zaffiro_700c_road_tire/pp.htm Just don't expect the best in flat protection, traction, or wear from them. Same with Michelin. Here are their low end tires: http://www.biketiresdirect.com/pmidyn/michelin_dynamic_tire/pp.htm And here is Continental: http://www.biketiresdirect.com/pcousw/continental_ultra_sport_(wire_bead)/pp.htm
Those lower tires are heavier, with wire beads and do not have as high a psi rating as you wish. The most (Conti) is 120 psi.