WordNet (r) 3.0 (2006):

push on
    v 1: continue moving forward [syn: press on, push on,
         plough on]

Moby Thesaurus II by Grady Ward, 1.0:

76 Moby Thesaurus words for "push on":
   accelerate, bundle, bustle, chase, crowd, dash, dash off, dash on,
   dispatch, double-time, drive on, expedite, fare, festinate,
   forge ahead, forward, get going, get moving, go, go slow, haste,
   hasten, hasten on, hie, hie on, hurry, hurry along, hurry on,
   hurry through, hurry up, hurry-scurry, hustle, hustle up,
   inch forward, journey, leap, lose no time, make haste,
   move quickly, muddle through, pass, plunge, post, precipitate,
   press, press forward, press on, proceed, process, push,
   push forward, push through, quicken, race, railroad through,
   repair, run, rush, rush along, rush through, scamper, scramble,
   scurry, scuttle, speed, speed along, speed up, spur, spurt,
   stampede, tear, travel, urge, wend, whip, whip along