Actually they could, and they did. The first person locked up for political purposes was a Pensacola newspaper reporter who printed something Braxton Bragg didn't like on the day after Sumter was fired on. Bragg threw him in prison.
Here are some details about this arrest of yours [Link]:
A man by the name of MATHEWS, the correspondent of the Pensacola Observer, under the signature of ‘Nemo,’ was arrested yesterday, and sent under guard to this city. The charge against him is furnishing information to the enemy. It was the intention of General BRAGG to make an attack upon Pickens on Friday night, according to this correspondent, and the information, after being published, was sent to the fort. Lieut. SLEMMER at once signalled the fleet, and during the day one hundred men were landed upon Santa Rosa Island, together with a large quantity of shot. Thus the plans of General BRAGG were frustrated. What will be done with this prisoner I am unable to say, but it does seem as if such important information ought to have been known only to the commander himself, until time to commence the attack. MATHEWS is now under examination at the War Department.
Some "political" arrest.