If those House members fight like hell with help from Trump/Cruz/Levin they can win this thing. They just need to fight like the democrats are fighting the defunding of Planned Parenthood.
They did fight like hell and they did win.
Anything in the ‘deal’ that Obama couldn’t do on his executive authority alone will be challengeable in court.
Without the Senate that is all that can be done, and Reid can block anything in the Senate.