The Nephites had essentially prayed for a miracle. What they got was Jehovah’s assurance that he would deliver them. There are certainly times in our lives when we need a miracle, and if we listen, we may get assurances that all will be well. Nevertheless, we still need to go, and do. The Nephites could not sit back and wait for a miracle. They took action, and took that action with the understanding that their God would preserve them. Jehovah gave them courage, not an immediate solution.
What the Nephites did was move around the city to create a real siege. They blockaded the pass with their troops so that the Lamanites in Manti would no longer receive supplies. That made a more difficult position for the troops in Manti. Therefore, they decided to go against the Nephites in order to remove the threat.