In a nutshell… maybe.
The 1st question is: do you “stand in the place of a parent” to your step-kids? The court will look at the parental relationship while you were a family unit, not after the separation. Factors to be considered are: do you discipline them? Do you show others that you are responsible for them? What is your relationship with them compared with that of the absent biological parent?
The 2nd question is: are there other persons who are/should be paying support for your step-kids? The courts have ruled in so many different ways on this one that it’s tough to give a straight answer. Some courts have placed the greatest support burden on the birth parents, while other courts have placed more importance on the step-parent who has the most involvement with the child.
The 3rd and final question is: if the step-parent must pay child support, what proportion should they take on as compared with the absent birth parent? Again, no easy answer, but some courts may order that the step-parent is only required to pay a certain % of the total support obligation, forcing pursuit of the absent parent to contribute the remainder.
So, in short, a step-parent may have to pay support for a soon-to-be-ex-step-child, but the final determination depends on your circumstances and your relationship with your step-kids.