The request for Postl's resignation stemmed from what Pulte considered a "massively failed deal" with Centex, where William Pulte's letter stated that shareholders lost more than $1.46 billion.
"We need someone on the board to work with them constructively. We will meet with them any time, unfortunately our calls haven't been answered," Pulte said.
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When Cramer asked Pulte if he would like to become CEO of PulteGroup, he responded "Absolutely not, no. Frankly, I'm not qualified to be the CEO of the company, but at the same time I can say that Mr. Dugas with all due respect, losing $500 million doesn't qualify you to run this company."
PulteGroup is the nation's third-largest homebuilder and was founded by William Pulte in 1950. He and five friends built a house near Detroit and sold it for $10,000. Six decades later, Richard Dugas now stands as the CEO and chairman of the board of directors.
Initial stock performance under Dugas was impressive, with PulteGroup shares more than tripling in just over two years. However, shares collapsed in 2007 going into the financial crisis and have not bounced back nearly as well as other major homebuilders, such as Lennar or D.R. Horton.
The conflict of leadership was ignited by the company's founder and his family against Dugas. The spat was thrust into the public eye in April when the company announced that Dugas planned to step down in May 2017, partially due to pressure from Bill Pulte and his ally on the board of directors, Jim Grosfeld.
Additionally, the company also announced it was trying to boot Grosfeld off the board at the annual shareholder meeting. In response, Bill and William Pulte published a scathing letter to the board reiterating disappointment in Dugas. Since then, Grosfeld has resigned from the board of directors.
"I recently recommended that Pulte should buy KB Home … but while I think that would make a lot of sense, I doubt an issue this contentious will be resolved that easily," the "Mad Money" host said.
In a statement released on April 11, a PulteGroup rep said, "We are disappointed that the Pultes continue to attempt to destabilize the company's leadership and derail our successful value creation strategy through their public statements. Their attacks bear little resemblance of the facts."
PulteGroup did not immediately return calls for comment from CNBC.