If I were a Phocian, Theban, Athenian, or Corinthian, etc, I have a hard time envisioning cheering for the conqueror who had conquered me only a few short years earlier.
They were not supportive of him at all. Almost immediately, Athens, Thebes, and Thessaly declared independence. His most immediate threat was Thessaly, which had an army occupying a pass between two mountains. He was advised to use diplomacy and make nice. Alexander, being Alexander, decided to march OVER one of the mountains and take Thessaly. The other's surrendered without a fight. Before his conquests of Asia, Alexander began a few campaigns in the Balkans. During this time, Thebes and Athens rebelled again due to a false report that Alexander had died. Alexander responded to the rebellion by razing Thebes and splitting its territory. Athens politely surrendered again.
When Alexander went on his conquest of Asia, Antipater was left in charge of Greece. Being one of the generals who had helped subjugate much of Greece, Antipater was no let well-liked in Greece. In 332 BC, Thebes revolted again, which provoked Agis III of Sparta to attack Macedon as well. They quickly took Crete and several other cities, sparking a real problem for Antipater.
Antipater pardoned Thebes. Having recently been razed, there was only so much damage Thebes could do, but fighting two enemies would have been more of a hassle if anything. After receiving money from Alexander, Antipater raised a force twice that of the Spartan army and went on to crush Sparta at Megalopolis, forcing their surrender and entrance into the League of Corinth. (In addition, the last stand of Agis III was truly one of the bravest last-stands in history. He ordered his men to retreat and held a mountain pass by himself, allowing his men to live another day.) This was a pretty big deal. Antipater had won against the SPARTANS. So that was pretty much it for revolts in Greece until Alexander died.
Alexander was actually very upset that Antipater had been able to win against the Spartans and hold Greece together so well. But we all know how Alexander could get.
As far as resentment goes, you'll bet there was a lot of resentment. Even his generals begged Alexander not to go on the expedition without a wife, but something tells me that just ended in eye-rolling. But the Greeks were under the direct rule of someone who beat Sparta while his boss was off carving a giant empire. They weren't going anywhere and they knew it.
Hope this answers your question!