Tunisia, formerly a French colony, strengthened ties with the US during WWII to help gain its independence which it did get in 1957.
France remained Tunisia's most important Western economic trading partner as well as military and financial aid. After independence, The US was quick to support Tunisia with economic aid. The US was caught several times in the middle of disputes between Tunisia and France but was able to maintain a consistent and stable relationship with Tunisia.
An Economic Hit Man Success Story
The US has always supported Tunisia with economic aid and military assistance when necessary. When Zine El Abidine Ben Ali took power via a coup in 1987, the US announced its support for the dictator. Tunisia continued to accept aid from the US as well as loans from the World Bank. When Tunisia couldn't repay their loans, they agreed to restructuring terms such as opening up their markets to US companies. This is the desired outcome to the US's preferred method of world influence. The US government has continued to support Ben Ali even through serious human rights issues and brutal state police.
Tunisia and Democracy
Tunisia has long had a secular pro-democracy movement which has been repeatedly repressed by Ben Ali. Even as the protesters demonstrated in the streets, the US government took a 'wait and see' approach as per Secretary of State Hillary Clinton:
we are worried, in general, about the unrest and the instability...So we are not taking sides in it...we have got a lot of very positive aspects of our relationship with Tunisia...I think we will wait and see. (http://www.state.gov/secretary/rm/2011/01/154295.htm)
US Embassy Cables from Wikileaks (http://www.guardian.co.uk/world/us-embassy-cables-documents/217138) reported:
The problem is clear: Tunisia has been ruled by the same president for 22 years. He has no successor. And, while President Ben Ali deserves credit for continuing many of the progressive policies of President Bourguiba, he and his regime have lost touch with the Tunisian people. They tolerate no advice or criticism, whether domestic or international. Increasingly, they rely on the police for control and focus on preserving power. And, corruption in the inner circle is growing. Even average Tunisians are now keenly aware of it, and the chorus of complaints is rising. Tunisians intensely dislike, even hate, First Lady Leila Trabelsi and her family. In private, regime opponents mock her; even those close to the government express dismay at her reported behavior. Meanwhile, anger is growing at Tunisia's high unemployment and regional inequities. As a consequence, the risks to the regime's long-term stability are increasing.
I guess we'll all take a 'wait and see' approach to see if the US government supports democracy in Tunisia. To be sure, the US government has a strong influence on what will actually happen in Tunisia.