So he really didn’t have that much of a problem with outrunning his logistics, did he?
Once Grant crossed the Mississippi River on the 29 April, he was not resupplied until he started the siege of Vicksburg on May 18. In that 20 day period his army fought 7 battles, captured Jackson MS. and finally laid siege to Vicksburg. Grant’s army strength was about 77,000 men. When Lee went into Pennsylvania, he had a wagon train 25 miles long to support his army of 75,000 men.