Ineos, who own the plant, has given its 1,350 employees until 6pm on Monday night to agree to a new contract with less favourable terms and conditions or face redundancy.
The Switzerland-based privately owner firm says more than 250 workers have already signed the new contract, which is claims is needed to prevent permanent closure of the refinery.
However, Sheridan, writing in her exclusive Evening Times column, has urged workers to continue their battle to defend union organiser Stephen Deans and oppose job cuts.
She said: "I know it can be unpopular but when it comes to trade union disputes and industrial actions I am firmly on the side of the workers. I have been in their shoes many times. Attacked for standing up for wages, pensions and in support of fellow members.
"It's never easy to strike. In fact it's terrifying. But sometimes you have to make a stand. So I want to offer my support to the Unite members at Grangemouth, the posties who will be striking on November 4 and other trade unionists forced into action."
Workers held a rally at the refinery yesterday. On Saturday, First Minister Alex Salmond told Ineos "to fire the plant up and fire it up now" and urged both sides to negotiate.
However, despite union and management welcoming his intervention, neither last night appeared ready to budge. Instead, the two sides are still fighting to convince employees each offers the best long-term solution to what is Scotland's single most important economic asset.