Given the tight controls of media and information in general in Khartoum, outside observers are forced to make their own conclusions about what the people think of their leadership and the ICC in particular.
In my conversations with both foreigners and Sudanese, these opinions vary dramatically. All of the outsiders' opinions, though of course not nearly as succinct or in contact with the realities as the Sudanese, have at least a kernel of truth to them.
There's an interesting Sudan Tribune article on the subject today that is absolutely worth a read. Though just a random "man-on-the-street" grab of opinions, it is quite telling. Read the article here.
My opinion, which I'll admit is simply one of many, is that the supporters of the regime are those whom rely on it for its largesse. With the pool of money shrinking, and the cost of support increasing with Sudan's inflation, there is a coming point when the regime will simply be unable to pay supporters to support it.
Here's some backgound observations on the economy in "the north": Since the late 80's and early 90's Sudan's independent upper and middle class have had their professions, assets and businesses either stripped, nationalized, radically devalued, or sidelined by government policies. The regime sought to stifle pockets of competition from political, economic, academic and professional circles and created an environment that made competitors dependent on party affiliation for jobs, economic opportunity or safety from military service that could be a death sentence. I've seen this first hand: businesses exhausted by lack of government 'permits' and competition by regime-affiliated companies, the middle class struggling to live on 1980's-level wages, and ever-dwindling avenues for private wealth development. It's evident that the productive classes of the society are being deliberately boxed-out and impoverished.
Jumping back to the ICC issue, I believe that the only life raft President Bashir can cling to now is nationalism. Nationalism, led by the party and its recipients, as a defense to this situation is going to have to be big, expensive, and kept at a fast jog -- in perpetuity. The regime uses rallies to demonstrate support. The bodies in the rallies are those of supporters from within the government and parastatal companies. If they are on the street dancing with the President, they aren't being productive. Can this task be borne by the regime? I don't believe so.
The fall back to this option with be the regime using the lash to keep its population in check. It does so to some degree now, but like the reliance on nationalism, that is usually to the massive detriment to the economy. Strikes, shunning by world markets, reliance on a single commodity for foreign currency inputs, economic sabotage and the typically poorly run parastatal organizations will cause the economic downturn to accelerate.
Lost government revenue, the high cost of a security/military apparatus fighting the population, and lost revenue to regime supporters, will eventually force regime leaders to make tough decisions. That will likely mean either putting President Bashir out to pasture and re-creating the political environment to allow economic breathing room, or simply sinking the whole ship of state.
Given the actions by the NCP in the past 20 years, I would not place a wager on which direction they will take.