squeak by/through, to succeed, survive, pass, win, etc., by a very narrow margin: They can barely squeak by on their income. The team managed to squeak through.
Origin: 1350–1400; Middle English squeken, perhaps < Scandinavian; compare Swedish skväka to croak
late 14c., probably of imitative origin, similar to Middle Swedish skväka "to squeak, croak." The noun is from 1660s; sense of "narrow escape" is from 1822. Squeaky clean in fig. sense is from 1972, probably from advertisements for dishwashing liquid.