List two examples used by the authors to illustrate the precarious nature of the new country in 1789

Tallmadge Amendment 1819. Missouri territory wants admission as a slave state. The House of Representatives (dominated by the North) passes the Tallmadge Amendment, which attempts to curb Missouri slavery. The South did not want the precarious free/slave state balance in the Senate to tip in favor of free. The Tallmadge Amendment brought up concerns that Congress would abolish slavery everywhere.

Your question is incomplete but I will try to answer. Early countryhood proved very precarious for the United States. First, it is the first country with a modern democratic constitution as its supreme law, a novelty at the time where countries are under the heavy-handed rule of kings or royalty. Taxes, the new government feared that taxes might instill rebellion, but were needed to pay national debt. It culminated with the Whiskey Rebellion. The new nation also feared invasion (again) by Britain, and this fear was averted by the signing of the Jay Treaty normalizing relations between the two countries.