The Iranian regime does have some support base. There are differences in the percentage, with some people counting a support base of as much as 9% to 10% of the Iranian people.
In general, I can sum up the reaction of the Iranian people, especially those who oppose the regime, as indifference. However, those who do support the regime are in a very celebratory mood, because after over 40 years of self-declared war against Israel, finally the regime had a chance to launch missiles, drones and cruise missiles from Iranian territory against Israel proper. That was considered a major achievement, given that ultimately the Israeli response was very measured. Those who supported the regime were very happy about it, and obviously the majority of Iranian people who did not support the regime were indifferent—or, in many cases, they went on social media to offer support to the Israelis.