This happened around 1800, when the USA was growing. The first state to have no property requirements for voting was Vermont, when it joined the union in 1791. So it was not really a matter of "abolishing" those restrictions as of not introducing them in the first place - most new states follwed suit. I think the first state to abolish existing property requirements was New Jersey in 1807 (ironically, at the same time they removed women's suffrage).
The last state to remove property requirements was Rhode Island in 1843, and it took a rebellion to achieve that, and even then the requirements were only dropped for USA-born men, not for immigrants (that took until 1888!).
So it pretty clearly was controversial, and the movement towards extended suffrage is strongly associated with Andrew Jackson and the budding Democratic party, but it's a bit more complicated than simply "one party was for it and the other against", especially since at that time the landscape of political parties was still in flux: the Republicans did not exist yet, and instead the Federalists were still around and the Whigs formed as an opposition to Jackson.