Doubtful it would help. First, they would have to write a law to counteract the executive order, then get it passed through both houses of Congress then get the President's signature or override his veto. Since the Democrats will either continue to have majorities in both chambers or, at the very least, be able to sustain a veto override, it wouldn't be worth the effort unless the EO was so offensive that even a large contingent of Democrats believed it went too far.
Right now most any thing he does is offensive. Since the gains the Republicans will make will most likely come at the expense of Blue Dog Dems, the Bernie Sanders wing of the Democrat party will dig in their heels.