2:30pm update:

We are keeping a close eye on storms that are developing over Ogle and Lee Counties across northern Illinois. Right now, these storms are producing a little bit of lightning. The National Weather Service did put out a Special Weather Statement around 1:40pm.

The Special Weather Statement was issued due to conditions that are favorable for funnel cloud development and even brief landspout tornadoes. These are shorter lived and less intense than supercell tornadoes. The main area we are watching for development are Ogle, Lee and DeKalb Counties.
Midday update:

Most of northern Illinois is still included in a low-level risk of severe storms late Tuesday afternoon into the early evening. The timing would roughly be between 3-8pm for any severe storms to move through the Stateline. Threats include hail along with heavy downpours, though funnel clouds and even isolated brief tornado touchdowns cannot be ruled out because of our cold core set up and surface-based convergence.

Chances of rain and even a few storms will linger into Wednesday behind the low but anything we see after tonight would not be severe. The severe threat will shift to our southeast tomorrow. A few spotty showers could last into Thursday, but we will see clouds quickly decrease Thursday evening and that will pave way for sunshine to return Friday and temperatures to warm back up above normal.