Now you are just spouting democratic party line. If the House don't appropriate it, they can't spend it. Painful, you bet but they have the Power of the Purse. It might behoove you to re peruse the Part of the Constitution where they say no Congress can bind a future Congress.
The House of rep’s has ALREADY appropriated funding for ACA back when Pelosi was the Speaker of the House.
Again, the House has the responsibility to initiate spending proposals. It can not pass any law all by themselves without passing the senate and signed by president.
To stop funding ACA will require either modification or repeal of the law. That requires senate to vote for it and the Bozo in WH to sign it.