Two weeks ago at a “tea time” at Twitter, co-founders and directors Jack Dorsey and Evan Williams — a pair who have not always seen eye to eye over the years — joined together in solidarity in front of the employees at its tony San Francisco HQ.

Their message, according to many there? That they and the board of the social communications company were “super supportive” of CEO Dick Costolo, who shared the stage with them.

Taking questions from general counsel Vijaya Gadde about the ongoing swirl around Costolo’s performance as a leader and how he has been under fire from Wall Street of late, both Dorsey and Williams noted that they were not ignorant of the investor pressure over a variety of issues from lackluster product innovation to management turnover to worries about user growth.

But, they tried to reassure staffers, they said they believed in the plan that Costolo was spearheading and the direction Twitter was headed in under his guidance.

That message of support got even more public this week, as Dorsey took to Twitter to defend Costolo again, following up on another earlier similar tweet by influential board member Peter Currie.

“As for @dickc,” wrote Dorsey. “Our cofounder @ev rightly pointed out there isn’t a single person who has been thinking longer about Twitter than @dickc.”

Why all the noisy support? Perhaps, said many sources with knowledge of the situation, growing worries about potential attacks from activist shareholders. Thus, a goal to try to shut down the conversation around Costolo’s efficacy.

“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.”

Some have been running hard at Costolo for a while now, including Jim Cramer on his influential CNBC show “Mad Money,” who has put an ongoing focus on ousting Costolo. He backed off slightly at the beginning of the year, noting: “I’m done. I’ve made this resolution that I’m going to be much kinder about Costolo, and he can stay.”

But soon after, Cramer was back, crowing: “ABC — Anybody but Costolo.” (When I saw him recently in New York, he cackled at his pun, but added that he is only bringing this up over and over because he believes Twitter has huge potential not realized.)

However it is delivered, this is clearly unneeded noise for Twitter and can build momentum in a very real way. Sources, for example, said a number of former employees are getting pinged by hedge funds about Costolo, who appear to be doing extensive research on him.

For example, one former Twitter exec recently got a note from a researcher at Stephen Mandel’s Lone Pine Capital.

“I’m writing you because we are trying to profile Twitter CEO Dick Costolo in light of a number of executive departures over the past year and questions about the company’s performance,” said the email sent via LinkedIn. “I am interested in discussing your impressions, observations and experiences working at Costolo and nothing else … I would greatly appreciate any insight you can provide.”

While a real challenge has not appeared as yet, some insiders do say that Twitter is vulnerable to attack, especially since it does not have a dual-class stock structure.

“This single class of shares makes Twitter inherently reactive to investors on the plus side,” said a source. “And, on the down side, very susceptible when things are not going well.”

Actually, according to a report from takeover defense site, SharkRepellent.net, Twitter is not an easy company to effectively attack, including having the unilateral right to issue preferred shares with special voting rights without shareholder approval. And more: The company has a staggered board of directors, shareholders cannot call a special meeting to effect change and, perhaps more importantly, it is already past the deadline for shareholder proposals for this summer’s annual meeting.

Said one takeover defense source: “The only real pressure that can be brought on Twitter by an activist in the near term is one of public shame.”

But that scenario is not uncommon. Both Tim Armstrong of AOL and Marissa Mayer of Yahoo have most recently seen activists come after them in that manner and to some impact. Most agree that Mayer’s recent move to spin off the company’s 15 percent stake in China’s Alibaba Group to shareholders is a direct result of public pressure from Starboard Value to do so, a sentiment which caught on quickly with her bigger investors.

What they want from Costolo is a little harder to grok, as it is harder to force someone to create a better product or make more people sign up for the service. Beyond the board deciding to replace him, which might only result in more chaos, it’s not clear what the goal would be.

Well, there is a eternal goal of manipulating the stock. All the rumors floating around related to Costolo — from him immediately stepping down at various times or Google buying the company, two recent ones that seem less than accurate — currently seem more designed to do that as they are eagerly lapped up by the media and regurgitated.

Still, in real terms, there is no question that Costolo continues to be under pressure, leading up to its earnings report next week in which Wall Street is expecting to see some improvement in Twitter’s performance.

Said one person close to the company about the dangerous swirl that Twitter has been pulled into: “Dick has nine lives, but he might be on his eighth at this point.”