Inter Milan perhaps failed to convince better coaches to take over this head coach position after Inzaghi departure but it does not mean they will accept too poor performances from Chivu. The match with Juventus will be a big test for Chivu and Inter Milan under his management, and support from Inter Milan might drop considerably if Inter Milan loses this important direct match that has value like a 6-point match.
Inter Milan actually knew risk of believing in a young and inexperience coach like Chivu but I believe that they did not reduce their targets in the season like no Scudetto, no Champions League title. Chivu with 1 win, 1 defeat after two matches, has still been not in too bad situation in the club. However, it will change considerably if he loses in a coming big match with a direct competitor for Scudetto and top four, Juventus. This defeat if happens, will put Chivu under a lot of pressure, uncertainty in the club and perhaps a tough decision can be made, firing him after only three matches in Serie A, is not a kind of impossible scenario.
Chivu is very likely in an uncomfortable situation that could lead to a very difficult decision by the club who might already want to sack him, but the key moment will be against Juventus in the Derbie d'Italia which will take place in a few weeks, we will see what will actually happen.