Not just “best in the game right now”; Maddux's 1994–1995 is arguably the best two-year stretch any pitcher has had in MLB history (up there with Pedro's 1999–2000 and Walter Johnson's 1912–1913).
I'm a very small Hall person in general; to be a HOFer, you should be one of the top 2 players at your position for a decade, give or take. Or you should be someone who would normally be that, but for playing during a time that's particularly deep. Or you should have an outside impact such that your Fame exceeds what would be indicated by purely on-field performance.
Brees is pretty much the definition of a borderline candidate to me. He never met the former criteria: Brady/Manning in his early career and Brady/Rodgers in his older years were a tick ahead of him. And he isn't someone who's going to gain bonus Fame points based on outside factors: he's not Unitas revolutionizing the passing game, or Jackie Robinson breaking the color barrier, or Jordan marketing the NBA at a high level (not that they necessarily need bonus points, but they've got them to spare).
The middle factor is debatable; I could go either way. Between Marino, Montana, and Young, he's probably #3 in the league again for most of the 80s and 90s, though. I probably put him in, just based on QBs being important enough to be slightly overrepresented relative to other positions, but I wouldn't cry if he didn't make it.