Palpatine's plan to become emperor started when he ordered the Trade Federation to blockade Naboo etc., and he therefore started the Clone Wars. The extent of his plans, however, seem to rely on him being in control of both sides of the war - what if he was not elected chancellor, or if Padmé didn't vote out the old chancellor? Did he have a backup plan with the same outcome, becoming emperor?
I'm not aware of a specific statement that Sidious had a backup plan, but he had multiple routes to transform the Republic into the Empire with himself as Emperor.
For example, it was Sidious' apprentice Tyranus (Dooku) who recruited Jango Fett to be the template of the clone army that was originally ordered by the Jedi Master Sifo-Dyas (who was killed shortly after he ordered the army). Tyranus (and therefore Sidious) thus had control of the clone army (which the Republic wasn't even aware of until just before the beginning of the Clone Wars), so had Sidious not become chancellor he could have used the clone army combined with the droid armies of the Trade Federation and any other separatist groups to launch a massive attack on the Republic. The Republic would have had no army to oppose them since the Senate opposed the Military Creation Act up until the beginning of the Clone Wars (and even then, the Military Creation Act was Sidious' initiative to use the clone army for the Republic). This route would have constituted a hostile takeover of the Republic instead of destroying it from the inside like Sidious actually did. The main problem with this route is that it would have been much more difficult to eradicate the Jedi Order since Sidious would not have been able to surprise the Jedi with Order 66 -- he would have had to rely on killing the Jedi by the sheer number of clones and droids attacking them.
Even with the hostile takeover route, Sidious had ways to hurt the Republic from the inside as Senator Palpatine. We are told in Episode II that
so clearly Palpatine had considerable influence in the Senate, which he could use to further destabilize the Republic even if he was only a Senator and not the Supreme Chancellor. Using the hostile takeover strategy, for example, Palpatine would have influenced the Senate to oppose the creation of any army until it was far too late to oppose the separatists.
That said, Palpatine's election to the Supreme Chancellorship was quite certain. As previously mentioned, Palpatine was able to achieve considerable influence in the Senate and he no doubt waited until he had enough influence to be electable. This influence, combined with the sympathy he gained from the Trade Federation's invasion of his home planet, meant that Palpatine would almost certainly be elected. Palpatine really engineered his election -- it wasn't like he left to it chance.
If he had not been made Chancellor (and then Emperor) at that time, he would have simply continued to undermine the Republic from his vantage point as Senator. He knew it was just a matter of time before he could seize total power (if he could keep his efforts hidden from view). It was inevitable considering the bloated, ponderous and inept bureaucracy the Republic had become.
This answer, though opinion based, is derived from decades of dealing with sneaky slimy people who are artists at diverting attention away from their nefarious activities and providing themselves 'plausible deny-ability' if challenged. The Sith are such characters.