Mrs. Bachmann is correct in that the Islamic Republic of Iran sees itself as an exporter of Islamic revolution and the constitution does indeed call for Jihad. From the constitution discussing the purpose of the military:
Accordingly, the Army of the Islamic Republic of Iran and the Islamic Revolutionary Guards Corps are to be organized in conformity with this goal, and they will be responsible not only for guarding and preserving the frontiers of the country, but also for fulfilling the ideological mission of jihad in God's way; that is, extending the sovereignty of God's law throughout the world (this is in accordance with the Koranic verse "Prepare against them whatever force you are able to muster, and strings of horses, striking fear into the enemy of God and your enemy, and others besides them" [8:60]).
However, the Caliphate is a Sunni tradition long abandoned by the supporters of Ali (those who would become Shia). Shia, which comprise the majority of Iran's population, believe in Imams descended from Ali. Iran's official denomination of Shia, Twelver, believe the twelfth Imam is currently hiding and will come again. Iran's Islamic government sees itself as a placeholder until the Imam's return. The Caliphate, an institution which any Sunni can become leader but in practice has been restricted to feuding Arab and Turkish families, has been denounced throughout history by Shia theologians.
If Bachmann wanted to warn about Shia Islamism she has solid ground in the Jihad passage of Iran's constitution. Her argument though is greatly weakened by her warnings of Shia supporting the Caliphate.