The Teamsters urged the smaller union to hold a secret ballot on whether members wanted to continue striking. Many workers in the bakers union decided to cross picket lines last week but Hostess said it wasn't enough to keep operations at normal levels.
Teamsters General Secretary Ken Hall said the failure of the mediation talks Tuesday and the likely shuttering of the company was a "tragic outcome" for Hostess workers.
Rayburn said that Hostess was already operating on razor thin margins and that the strike was the final blow. The bakers union meanwhile pointed to the steep raises executives were given last year as the company was spiraling down toward bankruptcy.
The company's announcement last week that it would move to liquidate prompted a rush on Hostess treats across the country, with many businesses selling out of Twinkies within hours.
Even if Hostess goes out of business, its popular brands will likely find a second life after being snapped up by buyers. The company says several potential buyers have expressed interest in the brands. Although Hostess' sales have been declining in recent years, the company still does about $2.5 billion in business each year. Twinkies alone brought in $68 million so far this year.