A number of Islamic parties and political groups have called for the restoration of Caliphate. It is a clearly and often repeated stated goal of al-Qaida. It would have an elected or appointed Caliph and a Parliament (Majilis al-Shura).

The Caliphate does not call for some kind of supreme dictator, with total authority, demanding slavish obendience from the people in service of the state. There are provisions for accountability of rulers in the Caliphate.

http://en.wikipedia.org/wiki/Caliphate
Sunni Islamic lawyers have commented on when it is permissible to disobey, impeach or remove rulers in the Caliphate. This is usually when the rulers are not meeting public responsibilities obliged upon them under Islam.

Al-Mawardi said that if the rulers meet their Islamic responsibilities to the public, the people must obey their laws, but if they become either unjust or severely ineffective then the Caliph or ruler must be impeached via the Majlis al-Shura. Similarly Al-Baghdadi believed that if the rulers do not uphold justice, the ummah via the majlis should give warning to them, and if unheeded then the Caliph can be impeached. Al-Juwayni argued that Islam is the goal of the ummah, so any ruler that deviates from this goal must be impeached. Al-Ghazali believed that oppression by a caliph is enough for impeachment. Rather than just relying on impeachment, Ibn Hajar al-Asqalani obliged rebellion upon the people if the caliph began to act with no regard for Islamic law. Ibn Hajar al-Asqalani said that to ignore such a situation is haraam, and those who cannot revolt inside the caliphate should launch a struggle from outside. Al-Asqalani used two ayahs from the Quran to justify this:

“...And they (the sinners on qiyama) will say, 'Our Lord! We obeyed our leaders and our chiefs, and they misled us from the right path. Our Lord! Give them (the leaders) double the punishment you give us and curse them with a very great curse'...”[33:67-68]

Islamic lawyers commented that when the rulers refuse to step down via successful impeachment through the Majlis, becoming dictators through the support of a corrupt army, if the majority agree they have the option to launch a revolution against them. Many noted that this option is only exercised after factoring in the potential cost of life.

The way they imagine the Caliphate doesn't sound much like either of the fascist systems headed by Hitler or Mussolini to me.

"Islamofascist" seems to more or less mean, by those who use the term, "any Muslim who we are fighting." Whether this enemy envisions forming a state based on fascism, or not, seems to be irrelevant. There is considerable stigma attached to the name and to the concept, and it is not uncommon for people to label their political opponents (or authority figures in general) pejoratively as "fascists".