The U.S. Army in 1861 was tiny and mostly stationed in the far west on the frontier. It was absolutely dwarfed by the volunteers that the Confederate and U.S. political system could summon. As such, the U.S. Regular Army was by design simply incapable of interfering in politics.

U.S. Army, by which I mean regular army, strength in 1860 was approximately 16,000 men. Adding in the Navy and Marines it was still only 25-26,000 men. At the time of Fort Sumter, South Carolina deployed approximately 6,000 troops in the Charleston area alone, dwarfing the fort's garrison of 85 military personnel. After Fort Sumter, Lincoln called for and received 75,000 volunteers effectively a 5x increase in army strength which was soon matched by the Confederacy. By the start of 1862, the U.S. volunteer forces numbered over 500,000 troops in total, a 32x increase from their number at the start of 1861. Confederate armies nearly matched this increase.

The fact that American politicians could quickly raise far more troops than the regular U.S. Army was not an accident. This was a deliberate feature of the U.S. political system in the early to mid 19th century. With no strong opponent on the borders, the prevailing American political ideology viewed a standing army as dangerous and unnecessary. A volunteer force raised quickly in an emergency was viewed as safer and more democratic than a large establishment of professional soldiers. In many ways, the U.S. did not entirely change it's mind about this until after WWII, although it did become more sophisticated in its plans to mobilize civilians as soldiers in an emergency.