The U.S. Constitution is not the problem. Congress abdicating there powers, and backing up the courts as needed. Judges writing law instead of just interpreting the law. The executive branch does not get to pick and choose what laws to implement and ones to ignore. The executive branch wins on the element of time.
Congress has to back up the court rulings because the court has no enforcement powers. They have no sheriff or police. The power of the purse is the power of congress. The next step is impeachment, not much room in between . The two thirds requirement is good for rational people. but not others. Ruling by executive order is not the way to get around congress, for not passing a bill you will not veto. Executive orders are for emergencies and short term. Closing down the government by either side is foolish.
The money for amnesty programs should now be dead. Laws that change the constitution should not be by executive order. On the other side the Affordable Care Act was rewritten by the court because they make it a revenue bill. Revenue bills originate in the House. The court has become a swinging gate where one vote will reverse the out come. Reflective of a divided nation. In the lower courts, for every two judges the decision can swing.
Congress is keeping the country going by too many concurrent resolutions. The final budget votes have been Christmas Trees with little debate on some parts. Reports from an inspector general or the GAO could be used as a warning for problems in an agency. Congress needs to see if compromises that helped a bill get passed are ignored. Are executive orders and choosing not to follow passed laws breaking the budget.