Just because the COTUS does not result in the outcome you desire does not mean it is broke. It ever occur to you that maybe a majority or significant minority of citizens support continuing operations and that Congress is dutifully representing them?
Also, de-funding or not funding is a significant bar. It is used many times the other way around: Congress passes some popular law to get public support/accolades while not voting to fund it to keep any action from occurring. Congress can also use other legislation as leverage, blocking something the executive wants. IOW, there are plenty of means and plenty of power at Congress's disposal.
WRT to the indians, yes, there was always nattering going on about their disposition back East. Usually, to no purpose. Thing is, the Feds were rarely in the driver's seat. Up to the Civil War, it was state's militias and local ad-hoc military organizations that did the majority of the fighting. Toss in the large number of settlers who set up shop/farm, steadily pushing the frontier back. The Feds would come in afterwards to recognize facts on the ground.