Gannouchi's interim government was under heavy pressure to move faster towards democratic reform, and his departure may not end the protests, unless the entire cabinet changes course or resigns. It has released political prisoners and granted a general amnesty, but protesters want fundamental guarantees of human rights and a new constitution.
Before the last few days of marches outside the hated interior ministry, the epicentre of the January protests, hundreds of young people had occupied the courtyard outside Gannouchi's office last week for an indefinite sit-in.
"Hypocrite minister" was written in Arabic on the name plate in such a faithful copy of the size and style of the original words "prime minister" that the title looked official. On the opposite side of the courtyard the finance ministry sported a "democracy wall", where demonstrators drew slogans or glued lists of political demands.
The rising temperature has not escaped the US' attention. Rightwing senators Joe Lieberman and John McCain were in Tunis a week ago, and last Thursday the state department's top Middle East official, William Burns, held talks with Gannouchi, who served in the same job for more than 10 years under Bin Ali. Although all three men hailed the Tunisian revolution, there is little doubt they want to keep it as far as possible in check.
After Bin Ali fled, Gannouchi's government was given two months to implement reforms. With the deadline of March 15 nearing, two broad approaches have emerged. Conservatives, backed by old political and business elite and most of the print media, is to extend the interim government's term until presidential elections in July.
France and the US are thought to be pressing for the formation of a new centre party that will absorb leading members of the old ruling party, the RCD, and provide a good candidate for the presidency.
The secular left and the Islamists want deeper change. Along with the main trade union federation, they are displaying remarkable unity and recently formed a National Council for the Defence of the Revolution (NCDR).
Far more people were driven into exile or imprisoned for long terms under the old regime than occurred under Hosni Mubarak's rule in Egypt. Welcome parties still turn up at Tunis airport almost every day to greet returning friends and heroes.
After all their personal sacrifices, they are determined not to be cheated into accepting a system that amounts to a sanitised version of Bin Ali's rule, with only a mild softening of the old top-down political control and the same economic inequalities between the capital city and the provinces that sparked the January uprising.
They want power to be handed, on or before March 15, to a caretaker team of independent technocrats. They also want the NCDR to be given official status and the right to monitor the new government pending elections. These elections should be for a constituent assembly that will work out a constitution that enshrines all the basic civic freedoms as well as mechanisms to prevent or punish torture in prisons and police stations.
There is a widespread consensus that the old Islamist party, Al Nahda (Renaissance), is Tunisia's strongest political force. It is more powerful morally, if not yet organisationally, than its Egyptian counterparts because so many hundreds of members suffered torture and exile under Bin Ali, unlike the Muslim Brotherhood in Egypt which was banned but not brutalised (apart from very few).
Western leaders like to think that they are bringing democracy to less enlightened parts of the world. In Tunisia things look different. They see a West that supported a string of Arab autocrats and they remember how western countries led the boycott of Gaza after Hamas won the 2006 election.
With Al Nahda poised for a major role if elections are permitted in Tunisia, western governments face a new test over their respect for political Islam. Will they fail yet again?