Jim Paulsen, chief investment strategist at Wells Capital Management, figures that a run to around $45 would turn the rally from a welcome sign that the economy was firm, to a potential "problem for inflation." He points out that oil spent a good deal of time in this area late last summer, so a return there would begin to push headline inflation "back above where core [inflation] is now." In the latest core reading on personal consumption expenditures (the Fed's preferred gauge) was up 1.8 percent year over year, and core CPI gained 2.2 percent.
Read MoreSantoli: Battle-scarred bull market turns 7
If headline inflation were to break decisively above 2 percent, it could tilt the Fed-watching debate toward those who believe Chair Janet Yellen is inclined to try for a couple more rate increases this year.
Goldman Sachs economist Jan Hatzius has been in this camp for some time, calling the investor consensus "complacent" about the possibility of repeated rate hikes in coming months. He's been pointing out that the labor market continues to tighten and financial conditions have firmed up smartly. He also says that various measures of inflation expectations are artificially quiescent largely due to low energy prices.
His Goldman colleague Zach Pandl has tracked a tight connection between retail gasoline prices and various measures of inflation expectations, including the University of Michigan survey. Market-based indicators of future inflation embedded in bond prices likewise are quite sensitive to the action in crude futures, even on a minute-to-minute basis.
Of course, all of this could be moot if this vicious rally in oil prices proves a fleeting matter of short covering and unrealized hopes for supply cuts. There is already evidence that producers have taken advantage of the lift in more distant futures prices to sell production forward. This, in turn, lessens their need to cut production and could undermine the rally if supply stays high.
And, conceivably, the stock market could ultimately make its peace with a more resolute Fed that proceeds on its hoped-for path of policy "normalization" if it happens for the right reasons of sturdy U.S. growth and calmer credit conditions.
Read MoreArmageddon bull market continues to beat odds
Yet as things stand, traders seem unusually dependent on the oil-stocks correlation, so anything that disturbs the familiar interplay would invite at least a period of market unrest, given the broader environment of skittishness and loosely held investor convictions.