WTI crude's low for the year was $42.03, set in March, and Brent was at its low for the year when it reached $45 in January. Kilduff said a strong jobs report Friday could send oil lower, but so could a weaker report.
"No matter what the jobs number does on Friday. If it's weak, it will be negative for crude oil because it will take away hopes of good demand. If it goes up, there's interest rate policy. Either way, it should be bearish for oil."
He expects oil to take a run into the $30s as early as September or October when refinery demand drops, as the industry prepares to produce winter-grade fuel.
West Texas Intermediate crude futures Tuesday rallied nearly 1.3 percent to just below $46, after Monday's heavy selling. Brent crude was flat at $50.10..
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"I think for the short term, you (Brent) could always correct to around $47. If you get through there, you have a level of $49.50 and then you have a very big top around $54," said Peter Amandio of Chicago Energies on "Power Lunch." He noted that crude lost $12 very quickly on fundamentals and word of Iran returning to market
Amandio said a catalyst to push oil lower could be a rate hike by the Fed, which would also drive the dollar higher. "Forty-two dollars is a very big level, and if we do go through those levels, you could see the low 30s," he said.
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Morse said the global oil market is oversupplied by about 1 million barrels a day, and ultimately it will be rebalanced.
"Something clearly has to give at some point on the supply side. we're not seeing either enough of a demand pickup or a supply slowdown to get the market into a more positive mode," Morse said.
"A prudent analysis would say the market turned on a hair, and it will turn on a hair again. It's at a rough spot right now especially since financial markets are bearish. Their expectations are bearish and they'll help to drive the price down," he said.
Strategists watch the EIA weekly report for clues on the U.S. oil industry, which has become a swing producer of sorts. Last week's reports showed a decline to 9.4 million barrels a day in U.S. production from a recent high of 9.6 million.
But Morse said that doesn't mean the U.S. industry is curbing production yet, and it's not been apparent in monthly data. In fact, analysts say the shale industry has been able to maximize production despite the sharp cutback in wells.
"I don't know of any evidence to say there's rolling over," he said. "Even the more recent drop in production is more related to the maintenance in the Gulf of Mexico. ... There are a lot of things other than shale happening in the U.S."
Morse said he will be watching the crude import levels in the government inventory report Wednesday, amid signs Saudi Arabia has been sending more crude into the U.S., after its imports dipped down to 825,000 in December and January from more than 1.2 million barrels a day.
He noted that Saudi Arabia is losing its leadership in market share in Asia. In Japan, the United Arab Emirates overtook it as the lead exporter, and in May, its sales were second in both India and China.
"If I were they, I would feel anxious about a market share strategy that didn't succeed. Their production policy is more opaque than it used to be," Morse said. Saudi Arabia is now exporting a record 10.5 million barrels a day, and is also exporting more refined product from new refining capacity.
Saudi Arabia orchestrated OPEC's decision to end output quotas at its November meeting, which sent already falling prices much lower.
"There's close to a zero chance OPEC is going to act the way it used to," said Morse, noting neither Iran nor Iraq would cut back on production.
"Why would they relinquish a market share they can't easily get back, when demand rises again," Morse said.