In what way can the House of Representatives force the President to do anything?
Pretty much only through the power of the purse.
If the President chooses to violate the US Constitution and attempt to use the Treasury Department as his own funding source, then this is not a separation of powers issue. This is a clear violation of the US Constitution.
The SCOTUS must rule; it must enter the fight.
But, even then, what means does the SCOTUS have to enforce their rulings? None.
The US Governmental system assumes everyone wants to uphold the Constitution. What happens when that is not the case, and especially when it’s the executive who is simply going off as a lone ranger emperor?
At that point, the only recourse if for STATES to refuse to comply and for tax-payers to refuse to participate.
Impeachment is an option.
Congress (including and especially house republicans) have abdicated their budgetting duties to The Fed already. Congress has NO CLUE how much funny money the fed has printed up.