Oh yes the House GOP majority is so slender that it only needs a few to be peeled off and they'll be in all sorts of trouble. One of the reasons why they're having to do this via Executive Order isn't just that they want the Executive to reign supreme but that they also know that a lot of this would struggle to get through the House. It only needs a few Republican's to be peeled off and it's dead in the water. So rule by fiat will continue for the foreseeable as they won't go to Congress as it's too hard to win and the GOP Congressional leadership seems happy to have Congress denuded of any of it's actual functions beyond the bare minimum.The GOP majority in both Houses is small, so literally a handful of Republicans voting with the Democrats could pass a motion that opposes something Trump is doing. This has actually happened in the Senate with Canada tariffs and there is potential for Trump's legislation to be defeated if it goes to Congress.
That's broadly my understanding, though it has to be on a matter which is within the constitutional purview of Congress for them to be able to overturn the relevant Executive Order via legislation. Though technically a supermajority is not required I suspect one will be in effect needed as no doubt when the bill comes across Trump's desk to sign he will veto it requiring Congress to override the veto which requires two-thirds support of both House and Senate. So, even harder than just needing a supermajority in the Senate!However, as I understand it, overturning an executive order requires legislation to be actively passed by both Houses. That requires the Bill to go on the agenda in the House (controlled by the GOP Speaker) and to get a supermajority in the Senate (requiring more Republicans to vote with the Dems).