FDR is the one who could have done it. The obstacle is convincing him, not anyone else.
No. First of all, by then the Democratic party had long since committed itself to Philippine independence--and so had the Republicans in principle (though on a slower schedule). Second, southern Democrats, who were an important part of FDR's coalition, would never accept giving brown-skinned people such enormous political power in the US--and a lot of members of Congress who weren't even racist would balk at the huge change in the composition of the House of Representatives and the Electoral College (not to mention the enormous increase in US responsibilities in the Western Pacific at a time the country was in an isolationist mood, the reaction of the Filipinos themselves who neither expected nor wanted any such thing, the sheer lack of precedent for a state that far away from the mainland US and so close to another continent, etc.) The population of the Philippines by 1930 was over 13 million--greater than that of New York state, the most populous US state (with 47 electoral votes). Even Hawaii (largely for racial reasons) wasn't granted statehood until 1959, even though it would never have more than two US House members or four electoral votes, even though it had a much larger percentage of "white" residents than the Philippines, even though it was closer to the mainland and farther from Asia, even though its residents clearly wanted statehood, even though two presidents (Truman and Eisenhower) had supported statehood for years, as had the national platforms of both major parties, etc.
The notion that FDR was some kind of dictator who could get Congress to pass anything he wanted is nonsense, as the fate of the court-packing and executive reorganization bills showed. Prior to 1937, FDR himself realized the limits of his powers in dealing with Congress, and for example gave only passive support to World Court membership (which failed in the Senate). He failed to include national health insurance in the Social Security bill because of fear that opposition from the AMA would then drag the entire bill down to defeat. And of course he would not speak out in favor of the anti-lynching bill, lest he alienate southern Democrats. Yet anti-lynching laws, while they would alienate the white South, did at least have a substantial US constituency in their favor, especially among African Americans whose votes were crucial in close elections in many big northern states. By contrast, there was no popular constituency at all for Filipino statehood, and FDR would have had to be crazy to support it.