Should negotiators reach a deal for Iran to end its nuclear program, in addition to the increase in production, Iran could unleash an estimated 30 million to 40 million barrels of oil it now stores on tankers. Oil prices could immediately fall by several dollars if a deal were reached.
"It's a substantial amount of oil. It could potentially move the market out of this range to the upside, or downside," said Michael Cohen, head of energy commodities research at Barclays.
Strategists say there could still be a deal, but later this year. If so, Iranian oil would not hit the market immediately, but traders still anticipate some additional crude from Iran by the end of the year.
The market view has been that a deal would still get done. Yet talk from Iranian hardliners raised doubts about progress last week.
Iran's top negotiator was headed back to Iran sunday to consult with top leadership while U.S. Secretary of State John Kerry rejoined talks this weekend—for the first time in weeks.
"There's a lot of political capital invested at this point in getting a deal," said Cohen. But the pushback has come from both sides. Five former advisors to President Barack Obama sent a letter of concern that the U.S. could fail to reach a "good" agreement and that it risks making concessions that would weaken international inspections, a cornerstone of the earlier agreement.
Earlier this week, Iran's supreme leader, Ayatollah Ali Khamenei, said most sanctions should be lifted even before Iran dismantles nuclear infrastructure or allows international inspectors to verify it is keeping its commitments. He also ruled out freezing nuclear enrichment for as long as a decade and reiterated a refusal to allow military sites to be inspected.
Complicating the situation, Iran's parliament this week passed a bill banning access by International Atomic Energy Agency inspectors to those sites.
Again Capital analyst John Kilduff said if talks actually fell apart altogether, the price of oil could immediately jump $10 a barrel.
Read MoreCalculus on oil prices changes as Iran talks wobble
"The knee jerk is going to be higher (prices). Also, I would assume relations will deteriorate between the U.S. and Iran, and maybe others, and that will raise the security premium for potential military action that Israel will push for," he said.
A complete breakdown in talks between Iran and the U.S. and five other countries is so far seen as unlikely, but the odds have clearly increased.
Meanwhile, the Iran negotiations are causing barely a ripple in oil prices. The market is so well-supplied that a bombing attack on a mosque in Kuwait on Friday served only to add some support to prices in a weak market.
A surge in crude supply and bingeing by consumers has been keeping U.S. oil futures in the $60-a-barrel area. While strategists see higher prices for crude this year, many see the potential for a dip back into the $50s in the second half of the year if demand drops.
"There's not too much conviction in the market in terms of where we're going, and you have big support to the downside and big resistance to the upside," said Citigroup energy strategist Chris Main. He said also at play were macro factors like Greece, the U.S. dollar and volatility in the Chinese stock market, which plunged another 7 percent Friday.
Citigroup expects WTI to average $61 per barrel in the third quarter, and fall to an average $54 per barrel in the fourth quarter. It forecasts Brent at $68 in the third quarter and $63 in the fourth quarter. Barclays, on the other hand, sees lower prices of $55 per barrel for WTI in the third quarter, and then a $63 per barrel price in the fourth quarter.
Strategists and other experts who answered a CNBC survey this month predicted an average price of $60.81 per barrel for WTI—right in the middle of the current range. West Texas Intermediate crude futures have also held just below the 200-day moving average, at $62.35.
Read MoreCNBC survey: Here's where oil prices are heading