If you’re referring to the part in TPM where Queen Amidala moves for a vote of no confidence in Chancellor Valorum, if Palpatine was not elected Supreme Chancellor he would’ve caused another situation where the newly elected chancellor would have to be voted out and create another chance for himself to be elected. He would continue to do so until he gets voted in, and then the storyline continues from AOTC from then on.
Alternatively, although less likely, he would’ve taken control of the clone army (or commission the creation of one himself – he is rich enough to do so) and convinced the Trade Federation, et al, to lend him their Droid armies. With the sheer numbers and might of the combined armies, he would’ve eliminated the Jedi and all who opposed him, then established himself as the Emperor and reformed the Republic into the Empire. I believe that this option is less likely because his actions would’ve painted him as the bad guy from the beginning, and hence a stronger Rebellion will be formed against him, with the Rebellion gaining more support than what originally happened in the movies (he gained much of his power initially by playing the good guy which gained him more support than the Jedi and, I believe, consequently the Rebellion). His rule might eventually have been overthrown, even without the help of Luke Skywalker, and probably faster than in the original movies.