Keith Whittington usefully identifies two types of constitutional crisis:
Operational crises arise when important political disputes cannot be resolved within the existing constitutional framework. (p. 2101)
Crises of constitutional fidelity arise when important political actors threaten to become no longer willing to abide by existing constitutional arrangements or systematically contradict constitutional proscriptions. (pp. 2109-10)
In the context of Trump, an operational crisis would occur if Trump directed border agents to disobey a judicial order blocking his temporary immigration ban. The agents would then need to choose whether to obey the president or the judge, with perhaps no clear sense of the proper thing to do. Trump has not issued such an order. But the sense that we may be on the brink of crisis arises because he has personally attacked Judge Robart, who issued a nationwide TRO, and has laid the groundwork for a more vigorous attack on the independence of the judiciary if a terrorist attack takes place in the future. If Trump successful cows the judiciary or the judiciary stands up to Trump, then a crisis might be averted. Whether the outcome is good or bad depends on your view of presidential power.
A crisis of constitutional fidelity could play out as follows. Suppose it turns out that Trump really seeks to pursue the alt-right agenda of purifying America of foreign influences, starting with Muslims. The executive order, which was limited to only seven countries, was just the first step in a broader plan. If so, Trump repudiates a norm that is currently regarded as constitutional by the legal and political establishment: a norm of nondiscrimination on the basis of religion. (I think there is in fact some question whether such a constitutional norm exists with respect to foreigners not on American territory, but put that aside.) A constitutional crisis will exist if Trump has such a plan and seeks to carry it out, especially if he tries to extend it beyond the limited confines of the executive orders.
How might a constitutional crisis play out? It depends on how public officials and ordinary people react to the allegation that Trump (or other officials) have acted unconstitutionally. There are many possible scenarios (public demonstrations, government paralysis, etc.), but it seems premature to imagine them.
It is possible to think that constitutional crises are not bad but good. The crisis that led to the Civil War ended with the abolition of slavery. The crisis initiated by Franklin Roosevelt’s court-packing plan eventually placed the administrative state on a firmer constitutional footing. What is distinctive today, putting the earlier crises in sharp relief, is that the challenge to the status quo has been brought by the forces of reaction, with liberals on the defense.