A former, unnamed staffer to Newt Gingrich makes the claim at Gawker:
Newt employs a variety of agencies whose sole purpose is to procure Twitter followers.... About 80 percent of those accounts are inactive or are dummy accounts created by various "follow agencies."
Gingrich does have a lot of followers -- over 1 million.
Sarah Palin, by contrast, only has 600,000+, and she's a far more popular figure in the party, and her tweets tend to crash servers while Newt's merely, well, tweet.
A Gingrich spokesman tweeted (here and here).
@Gawker Gaffes. Hoodwinks readers. Insults 1.3 million .@newtgingrich .@twitter followers. Report is #rude #unfounded & #erroneous.
.@Newtgingrich's 1.3 million followers are legitimate. @Gawker 's "source" is not. Story untrue.
UPDATE: Ben Smith has a good theory on the million -- Twitter's whilom "Suggested User List".
Gingrich was over a million followers well before the campaign existed or had staff, for the simple reason that he was one of the chosen on Twitter's official "Suggested User List."
Twitter actually disposed of the list after Republicans complained (accurately) that it was very heavy on Democrats, but Gingrich and John McCain were among the minority.
The fact that Gingrich was pretty active and engaging on the service probably helped get him on the list and generate followers, but as Anil Dash noted, the "million followers" that came with the SUL were pretty much a fiction -- most of them weren't really interested -- and Gingrich's claim that they reflected grassroots popularity is also doubtful.