Here's an idea I've been cooking up for a few hours. In Australia, our Prime Ministers have the power to call a double dissolution. For context; our parliament is bicameral like yours. However the difference is that only half our senate is elected each cycle while our entire house of Representatives is. A double dissolution is where the Prime Ministers send ALL senators and House of Representatives to an early election.
So what if Presidents in America had the same power. That if a bill is vetoed twice, but appears towards the President a third time, he can call an early election for ALL senators, governors and members of the house of representatives. How does this effect history?