It's hard to say, as Garfield wasn't even in office long enough to even begin any major undertakings. However, he particularly supported a government-funded education system, particularly for African-Americans, who he believed were being denied their voting rights thanks to literacy tests in the south. However, it is doubtful that this would have passed. He may have gotten through with enacting Civil Service reform, especially after the assassination attempt which was essentially brought about by the ills of that system.
Civil service reform would likely have passed, considering the identity of the would-be assassin.