Compounding this was the Sega CD and 32X addons for the Genesis. Both were projects the scale of a new console, but they were built as addons to the Genesis so they limited their audience to people who already had a Genesis. Neither really brought much to the table in terms of software libraries; lots of Sega CD games were Genesis titles with red book CD audio instead of FM synth chip tunes, or the occasional FMV title.
Then they brought out the Saturn, which some people even bought. It was a Sega console that had no Sonic game.
So going into the Dreamcast, Sega had three poorly performing consoles in their back catalog. I don't think the Dreamcast could have been a big enough success to save Sega's console division, and especially not with Sony about to dominate the 6th AND 7th generations with the PS2.