Twitter insiders want to 'shut down the conversation' about getting rid of CEO Dick Costolo

Here is the clearest sign yet that management at Twitter is concerned that maybe, just maybe, angry investors will succeed in their bid to get rid of CEO Dick Costolo.

Re/code's Kara Swisher reports that insiders there want to "shut down the conversation around Costolo's efficacy." (Last week, for instance, we saw founder Jack Dorsey go to bat for Costolo.)

Investors are mad because TWTR's stock price is in the toilet and there are ongoing concerns about Twitter's ability to grow its users (or even whether they are being counted properly). It's not that people think Costolo is incompetent or has the wrong strategy. Rather, it's that the needed changes at Twitter don't seem to be coming fast enough. A year ago, Costolo told analysts he was ordering changes that would make Twitter easier to use and easier for new members to get aboard. The changes since then have been minor, however. Twitter is still complicated. Meanwhile, there has been a huge churn in the management ranks under Costolo. In the last year he has lost or replaced five execs who report directly to him, including the CFO and the product chief.

Here's the key quote from an insider, per Swisher:

"Once this starts taking place in a public way, it can become a self-fulfilling thing and, at the very least, it undermines the effectiveness of the organization, is undermining to his authority and is completely distracting," said a source. "So, you have to shore up and shut it down before it gets any legs."

Here's the TWTR chart of doom:

Disclosure: The author owns TWTR stock.