Since the term "counter-offensive" was used, I'll assume a sort of Red Dawn scenario (the good one), but with teleportation. A major and superior hostile army of unknown origin suddenly appears in Chicago and begins attacking outward.
The National Response Framework would be activated to coordinate effort. NSPD 51 would also be activated, most of which is classified. An attempt would be made to organize the evacuation of Chicago, but it would likely result in the biggest traffic jam in history.
While the US is prepared for smaller attacks, terrorist attacks, or nuclear attack, it is not prepared for a large, well-equipped hostile land army suddenly appearing simply because there's no way it could happen outside of sci-fi. While there are various forces ready to respond immediately, these small units would not last long against an attack of this scale.
The first organized resistance would be 12,000 officers of the Chicago Police, plus surrounding departments. The governor would activate the Illinois National Guard and ask for help from the Federal government and the surrounding areas. Elements of the Illinois National Guard would arrive soon after, specifically the 178th Infantry Regiment in Chicago itself. The Illinois Air National Guard has no combat units. If things are desperate enough Naval Station Great Lakes, a US Navy training facility, might get involved.
United States Army North is charged with the protection of the United States. The major challenge is not distance, but readiness. Its combat units are not on ready combat status. They would need some time to call in their troops, get their equipment out of storage, come up with transportation and operational plans, and get everything organized for transport. Fortunately transport over land is much simpler to organize than over the ocean and they could probably do it in days rather than weeks. Actually then driving to Chicago is fairly easy due to it being very well connected by road and rail.
The first major combat units available would likely be elements of cavalry, airborne, and Marine units which are more mobile and "expeditionary" in nature. Fortunately for Chicago, none of these units are currently deployed. 10-15 years ago a significant portion of the US military would have been busy in Iraq and Afghanistan.
Elements of the heavier units would arrive in the days and weeks to come. National Guard units would be nationalized into the US Army. Reserve units would also be activated, though they will take weeks to gather their men and equipment and organize, adding some 200,000 more soldiers. Additional units would likely be recalled from overseas taking a month or more.
Meanwhile USAF Air Combat Command would organize its continental air forces. First Air Force is charged with defense of the continental US, plus the Eastern Air Defense Sector. This is primarily Air National Guard (ANG) fighter wings operating F-16 fighter-bombers. The closest are likely...
Heavy bomber units of B-52s and B-1 units have the range to fly directly from their bases around the country as soon as they are ready. All 19 active B-2s are part of the 509th Bomb Wing in nearby Missouri. These expensive and limited assets are unlikely to be committed until there is more information about the threat.
The 24th Air Force would also mobilize for cybersecurity and the 25th for intelligence and recon.
More wings would respond as they organize and tanker assets become available. If the battle goes on long enough aircraft from the Boneyard would be reactivated.
US Navy carriers are normally the US's fire brigades, but no US carriers will be appearing on the Great Lakes. The locks of the Saint Lawrence Seaway can accommodate up to 740 ft, but a Nimitz class carrier is over 1000 ft and the Wasps are over 800. Instead, their ready air wings may be forward deployed on land.
All of the Navy's destroyers, cruisers, and littoral combat ships (except the Independence class which is too fat) could make the trip to provide fire support, intelligence, and anti-air. In addition, Chicago is in range of Tomahawk cruise missiles launched from New York Harbor.