There were only two candidates in 2004 who would have been competitive with the President. Retired General Wesley Clark and Senator Joe Lieberman. Clark offered the greatest contrast with Bush: he was against the Iraq war from the start and he positioned himself as socially progressive. Joe Lieberman was a moderate Democrat much like John F. Kennedy and Bill Clinton. Lieberman was always tough on national security where the Bush campaign couldn't attack him as weak, yet he offered a contrast with the President on domestic issues.
John Kerry lost to President Bush because Kerry had no record of accomplishment in the senate, he was not decisive, and he had a very liberal voting record. Dick Gephardt would have faced some of the same challenges, and John Edwards would have had to defend an even more liberal viewpoint and less experience. Howard Dean moved to the left to be viable in the Democratic primary, he was actually a more centrist Governor. His issue would have been a lack of discipline on his part.
The President's advantages were he had protected the homeland post 9/11 and the economy began to recover by 2004. He was seen as decisive and tough.
Wesley Clark (D) 50% 272 EV
George W. Bush (R) 49% 266 EV
George W. Bush (R) 49.8% 286 EV
Joe Lieberman (D) 49.5% 252 EV
George W. Bush (R) 51% 275 EV
Dick Gephardt (D) 48% 263 EV
George W. Bush (R) 53% 307 EV
Howard Dean (D) 46% 231 EV
George W. Bush (R) 55% 311 EV
John Edwards (D) 44% 227 EV