Saudi Arabia is the world's biggest oil exporter and it has taken on the lion share of the cuts. But he said Russia is the wild card, since it has begun to do better economically as crude prices rose and may not be as desperate to deal.
OPEC producers meet May 25 and could decide then to extend the deal to cut 1.8 million barrels a day, which started in January. Cohen said it's possible they could shorten the time frame of the extension or change the amount of oil that is being taken out of production.
"You have to question whether the Syrian situation has now become a proxy that divides them more than the low oil prices united them. So that's a big deal here," said John Kilduff of Again Capital.
On Tuesday, Dow Jones quoted sources saying that Saudi Arabia wants to extend the now six-month deal to cut production. Oil was temporarily higher on the report. Meanwhile, Reuters reported that OPEC members reduced output more than they promised in March, with 104 percent compliance.
This contrasts with comments just a month ago, when Saudi Arabia warned other producers to keep their commitments on compliance and said it was too soon to agree to an extension of the production deal.
"Now you're kind of placing a wedge between the key players because of this [U.S.] policy. The question is whether oil policy can be separate from economic or national security policy. I think it aligns in some places and it's a concern in other places. In history there have been many cases where OPEC countries were at each other's throats, but they were able to come to a deal," Cohen said. It was the heads of state that actually agreed to the first production agreement, not the oil ministers, he said.
"What really matters are three people – [Iranian President Hassan] Rouhani , [Saudi Deputy Crown Prince] Mohammed bin Salman and President Putin. If you figure out their positions, then you have a good idea of what's going to happen. I haven't seen a quote from any of those three lately," he said.
Cohen said another issue is what role U.S. shale will play. "They see rig count increase in the United States and forecasts by a bunch of tight oil producers that production should be higher ... so at some point the question of whether they continue this is going to hinge on whether OPEC wants to continue seceding market share ... to non-OPEC producers," he said.
"OPEC wants to rip off the Band-Aid as soon as possible, and allow the prices to move back up to the $60 range on the force of the market alone. They realize they can't do that if the deal stays in place and they all have to comply. Eventually the compliance is going to show that certain countries are bearing more of the burdens than others," Cohen said.
He said OPEC will extend the deal, especially if market fundamentals weaken ahead of its decision, as he believes.
"We're still of the view that we're going to see a sharp price rally at some point occur in this quarter, and we believe inventories continue to be drawn down."
Kilduff said he believes OPEC's high compliance will be the result of Saudi Arabia cutting more than required. "The real test is going to come as we get to these warmer months and do the Saudis ramp up production to meet their internal demand. On the surface, it will look like Saudi production is spiking. These are the easy days to comply with the deal. But the hard days are coming," he said.
Important for the market Wednesday will be U.S. Energy Information Administration inventory data, released Wednesday at 10:30 a.m. EDT, and OPEC's monthly report is also released Wednesday. The International Energy Agency releases its data Thursday.
Kilduff said the IEA report will be helpful when looking at global inventories, which seem to be falling.
Markets have also been watching North Korea, as the U.S. moves warships into the area.
"Any move on Korea will be seen as the market as bearish because it's going to impact market activity and mean in Asia," said
"We're seeing encouraging inventory reports. They've been building much less," said Ryan McKay, commodities strategist at TD Securities.
Cohen expects Brent crude futures to trade at $58 per barrel in the second quarter, but he also expects the international benchmark to dip in the mid $50s in the third quarter before rising in the fourth quarter. West Texas Intermediate crude futures should be about $2 lower.
Watch: Oil market focused on production cuts