The Spinners reached the Top Forty just twice in the 1960s: with "That's What Girls Are Made Of" in 1961, and "I'll Always Love You" in 1966. They had a bit of a breakthrough in 1970, when the Stevie Wonder-written and -produced "It's a Shame" became their first Top Twenty hit (funny how Stevie keeps coming up in these essays).
Three things changed for the Spinners in 1972: Obviously not a priority for Motown, they jumped to Atlantic at the recommendation of Aretha Franklin. At Atlantic, they were paired with the producer Thom Bell. And Philippe Wynne joined the group, becoming the de facto lead singer.
For the next five years, the Spinners were the most successful R&B vocal group in the nation, both in terms of hits and in terms of cultural impact. Ironically, for a former Motown group that had its roots in Detroit, they helped define the Philly Soul sound, and they had five Top Ten hits, including the Number One smash "Then Came You," with Dionne Warwick.
Wynne left the group in 1977 for a solo career (to be managed by Alan Thicke!), and with the Philly sound fading in popularity, that was pretty much it for the Spinners. They did manage a couple of Top Five hits in 1980 with medleys of older R&B songs, and they have continued as a touring act to this very day. But for all intents and purposes, the Spinners' Hall of Fame case rests on that 1972-76 peak.
It was an impressive stretch, but not really Hall-worthy, in my opinion. For one thing, the Spinners weren't all that involved in creating their own records: They didn't write or produce at all, at least not any of their hits. When that's the case, you need more of a catalog than what the Spinners had. With all due respect to Henry Fambrough, I vote NO for the Spinners. I was always more of a Stylistics man, anyway.