Gasoline demand in the week rose to 8.82 million barrels a day, but the four-week average is 8.53 million barrels, the lowest since 2003.
Kloza said there's nearly 18 million barrels a day of refining capacity, up 400,000 barrels from last year, thanks to refinery expansions. Refineries ran at 83.5 percent of total capacity on average, down 2.8 percent from the week earlier, and about 3.5 percent below what analysts expected.
"I have a lot more faith that refinery runs are going to increase than I do that gasoline use is going to increase to above last year's level," he said. "We can almost count that we're going to run more crude. … This is a little bit of a malaise, a little funky, a little bit of zombie consumption out there."
In a research note on shale production Wednesday, Goldman Sachs noted among its favorite refineries are Holly Frontier, Marathon, and Western Refining. Those stocks were higher as were Tesoro and Valero.
Kloza said it appears the impact of a spring swoon in the economy is impacting gasoline, but warmer weather may stir some demand, since it has been an especially cold spring.
(Read More: 'Spring Slump' Unlikely to Become a Stall)
Analysts have said some of the drop in demand has to do with consumers buying more fuel efficient cars, but there is also a correlation between high gasoline prices and a drop in driving. AAA in a survey this week of about 1,000 adults found 61 percent believe gas is too high when it hits $3.50 per gallon, and 86 percent said they respond to high gas prices by driving less. Ninety percent said gasoline prices are too high when they reach $4 a gallon.
AAA reports the national average price of unleaded gasoline is $3.51 per gallon, slightly higher than Tuesday but about the same as last week, and down from $3.66 a month ago. At this time last year, the pump price averaged $3.84 per gallon.
"We'll probably dip below $3.50 and that would be the first time since February," Kloza said. "I still think prices are going to be similar to last year. I think they're going to be biased to be slightly lower. The second phase of the year starts in hurricane season. We are more susceptible to spikes brought on by hurricanes (because) so much of our refining capacity is in the gulf."
Prices at the pump reached their low last year of $3.33,just before the Fourth of July holiday.
West Texas Intermediate crude rose above $90 per barrel Wednesday, but it is still down nearly 7 percent month to date. Brent, the international oil bench mark, was above $101, and RBOB futures, representing gasoline in New York harbor, rose about a half percent to $2.73 per gallon.
(Read More: Oil Slide to Continue as Demand Picture Weakens)
John Kilduff of Again Capital said oil could rise a bit more, but it's direction is, in fact, lower. "I think we're clearing a bit of an oversold condition after the big drop of the past week or so. Maybe we'll take a run at $92 before heading back down again," he said. "The drop is temporary. Gasoline supplies aren't bad but to break the back of $3.50 gasoline, we'd like to see them rise."
(Read More: Power Shift: Energy Boom Dawning in America)