In theory, 2 equivalents are needed to hydrolyze aspirin. The first equivalent will deprotonate the carboxylic acid portion of the molecule, while the next equivalent will hydrolyze the ester. Under mild conditions, the hydrolysis will be unlikely to occur, so you would just observe a normal acid-base reaction. The titration curve would look resemble the titration of a weak monoprotic acid.
In practice, you would use an excess of base to speed up the reaction, since lye is relatively cheap.