What fundamental challenge to the Constitution did secession and the doctrine of nullification pose?

Secession and annulment doctrine challenged the federal government's supremacy.

Explanation:

The constitution establishes the supremacy of the federal government. This supremacy states that what is decided by the federal government must be obeyed and followed by the state governments.

However, secession established that the southern states of the country disobeyed the federal government, rejected its supremacy and separated from the country, establishing the very government to which it would be submitted.

The annulment doctrine also challenged the supremacy of the federal government, establishing that a state could reject the federal government's decisions if it considered these decisions to be incostitutional.