Back in the heady days of early January, when Illinois had cracked the top 25 and we had no idea that Chicago would be subjected to multiple polar vortexes, I was thinking John Groce was just the right guy for Illinois. He runs good stuff. He knows how to recruit. He has the required over-the-top work ethic. Even his orange-sportcoat homage to Lou Henson fits just right. On top of all that, he had the Illini — who came tantalizingly close to the Sweet 16 last March — tracking for a second straight overachieving season. Even though icy shooting has plunged Illinois into a six-game (and counting) skid, I still like Groce’s long-term prospects for putting the fight back in the Illini. You’re only going to go so far with three players who have Big Ten experience, an all-freshman bench and only one player who comfortably answers to the description ‘‘scorer.’’ In a Big Ten that’s as top-to-bottom tough as it’s been for a long, long time, there are going to be growing pains with a group like that. The gloom-and-doomers are going to see a team that faces an uphill battle to make the NIT and they’re right. At this point, that would be an achievement. Considering that Illinois was 13-2 and ranked 23rd a few weeks ago, that’s kind of hard to swallow now. That said, it would be a mistake to think Groce isn’t building a solid foundation. This is not the situation Illinois was in the last time it lost six straight in February 2012, when Bruce Weber was on the brink of being fired. It is more like January of 1999, the last time Illinois lost seven straight — a number it could reach when it plays host to No. 15 Iowa on Saturday. That was Lon Kruger’s third season. Just as the recruiting downturn in transition from Lou Henson caught up with Kruger, the recruiting falloff that greased Weber’s departure is catching up with Groce.