Not the public at large but the “select” or “organized” state militias that eventually morphed into the modern National Guards: at what point did they stop reporting for duty with their privately owned guns and started being issued duty arms from a state armory?
In the Revolutionary War, militias were fairly undisciplined and poorly trained, and tended to get their backsides kicked when they came up against well-trained British troops. To be fair, Washington’s own army suffered from the same issue until they went into Valley Forge, where, in addition to starving to death and dying from disease and exposure, his troops got some proper training in military fighting and discipline from the French and Prussians. Only then could Washington’s troops effectively go toe-to-toe with the British.
In the War of 1812, miltiias in general continued to perform poorly, again suffering from poor training and a lack of military discipline.
In the era between the War of 1812 and the Civil War, militias continued to be poorly armed, poorly trained, and poorly disciplined. But they weren’t fighting highly trained British troops any more, so they fared a lot better. Instead, they often got involved in fighting between pro-slavey and anti-slavery groups in the western territories, which ended up being one of the big issues leading up to the Civil War.
Both sides in the Civil War expected the fighting to be fairly short. They learned quickly that this was not to be the case, and as the war escalated, both sides found themselves with a drastic shortage of weapons and well-trained men. The Confederacy had a notable lack of manufacturing ability, and relied heavily on imported weapons and captured weapons. The Union had better manufacturing, but was also plagued by weapons shortages. Both sides supplied weapons to militias whenever possible, but weapons shortages continued to be an issue all the way until the end of the war.
This trend of supplying weapons and training to militias continued into the Spanish-American war. Many militias were even absorbed into the regular army, and unlike today, they were allowed to keep their basic militia structure and their militia commanders.
ETA: The period after the Civil War was a bit “interesting” in the south with respect to militias. Many freed blacks were organized into militias and were ordered to watch over Reconstruction. Having few weapons of their own, they were obviously given weapons by the US government (mostly Civil War leftovers). In response to the black militias, many all-white rifleman groups formed in the South, and violence between these all-white groups and black militiamen was far from uncommon.