Looking it up, I see that the Robert E. Lee paddle-wheel could do about 16 mph up stream, and at 800 miles from Vicksburg to Chicago, that would seem to take about 50 hours, or a little over two days. Did they sail at night? If not, then double that to four days up and four days back.
Jackson is 50 miles from the Mississippi. two days up river meant supply ships would have had to run the artillery gauntlet at Vicksburg, going and coming. No wagons on Grants side of the river. Supplies for Grant did not come from Chicago. They came from St Louis. Fifty miles of enemy territory subject to cavalry attacks every mile of it. That meant Grant would have to divert infantry and cavalry to protect wagons. It was a logistics problem Grant solved by simply loading each soldier with 6 days of rations and 100 rounds of ammunition. Artillery limbers carried 40 rounds each. That was sufficient ammunition for infantry and artillery. Cavalry and artillery horses grazed. He did not need resupply during the campaign. Once he was at Vicksburg, the corduroy road across Miliken Bend was completed, supplies came by boat down river from ST Louis, were off loaded up river from Vicksburg, transported by wagon on the corduroy road across Milikin bend, loaded on boats and barges, ferried across the River down river of Vicksburg then carried by wagon to Grant’s Army around Vicksburg.