FDR got 60.8 percent of the vote with Coughlin supporting Lemke, a weird little man from North Dakota who had minimal national recognition and no political presence. Long would have taken a much larger chunk of votes than the 1.95 percent that Lemke won. FDR would likely still have won in the electoral college, but the experience would have had an effect on his presidency, I believe, and it would have set Long up for a rematch in 1940.
I really don't see it.
It's easy to give FDR a harder run through the White House than OTL, I just don't think Huey Long is the man to deliver it, you're dealing with FDR, after all, a man who despite his many flaws created one of the strongest and longest-standing political coalitions ever. It literally only fell apart nearly 20 years after his death during LBJ's tenure. That sort of thing is so rare as to be considered a miracle in Washington.
But you also have to consider that FDR's agenda, which while pretty moderate (giving the trappings of a welfare state to a country that had never had it along with government-directed spending projects), was
viewed as tantamount to revolutionary socialism by conservative (and indeed several not-so-conservative) aspects of American society. What I think the sort of backlash FDR's policies received was a demonstration of was primarily two things: that America was (and still is) a fundamentally conservative country in the economic sense, and that FDR was someone who had pushed the limits of what was then considered tolerable government policy, and he definitely found times where his policies (namely the NRA and court-packing) resulted in
major backlash from more than just a vocal minority of the population.
Huey Long was ultimately too radical for American discourse. He pushed the economic question far further to the left than what was acceptable at the time, he was hated in his home region of the South for his stance on the race issue (which is to say he wasn't racist enough), the party bosses among the Democrats hated him because he was an outsider who was willing to destroy party structure to achieve his own power, and in-general had a legion of potential enemies from either the Democratic or Republican parties who would happily tear him down.
Huey Long is, well, a longshot for the presidency. He can be governor of Louisiana (whether in formal title or de-facto) for as long as he can form a full sentence (and possibly even after), but his chances on a national scale against well-organized, well-funded political machines that will regard him as a non-compliant, and therefore a threat, are pretty minimal.
Also, someone like Father Coughlin has no real appeal outside of the urban East Coast and Midwest, antisemitism isn't really a mass-mobilizing sentiment in areas where there are no Jews.