Nearly 6 in 10 Americans, 59 percent, would support a plan to lift international economic sanctions on Iran in exchange for new limits on its nuclear program.
Those terms match the language of a tentative framework for a deal agreed to by international negotiators on Thursday.
Thirty-one percent are opposed to such a deal in the poll.
Democrats are more willing to support such a deal, with 68 percent in favor and 22 percent opposed. Republicans are more closely divided, with 47 percent in favor and 43 percent opposed.
But the poll also finds that Americans remain deeply skeptical that an agreement would keep Iran from developing a nuclear weapon.
Thirty-seven percent of Americans are somewhat or very confident a deal would prevent a nuclear-armed Iran, with 59 percent having little or no confidence.
The poll was administered hours before Tuesday's initial deadline to secure a framework deal. The Obama administration, negotiators from five world powers and Iran are moving to finalize a deal before June 30.
President Obama praised the outlined plan Thursday as a "historic" agreement to curb Iran's ability to obtain a nuclear weapon, while many members of Congress and other world leaders expressed doubts over the plan.
Israeli Prime Minister Benjamin Netanyahu said that his country's Cabinet was "united" against the Iran deal, and Arab allies of the U.S. have struck a cautious tone.
The framework deal would lift many international sanctions on Iran in exchange for scaling down its number of installed centrifuges and allowing for international inspections.
The poll also indicates that a deal, which has become a second-term legacy issue for Obama, could play into the 2016 presidential races. A plurality of those surveyed, 49 percent, say the next president should favor a negotiated agreement with Iran, with 42 percent opposing.
Here are other key findings in the poll:
1. U.S.-Israeli relations
Half of Americans disapprove of the way Obama is handling U.S.-Israeli relations, compared to 38 percent who approve, according to the poll. That's driven mostly by Republicans, 86 percent of whom disapprove, compared with 21 percent of Democrats. Meanwhile, 44 percent oppose Israeli Prime Minister Benjamin Netanyahu's handling of the relationship, compared to 37 percent who approve.
Tensions between the U.S. and Israel appeared to escalate leading into this week's deadline for a deal.
Top Obama officials skipped Israeli Prime Minister Benjamin Netanyahu's March 3 speech to Congress, held two weeks before Israeli elections, and the White House criticized Netanyahu over his pre-election remarks on a Palestinian state and Arab-Israeli voters. The poll found 39 percent support recognizing a Palestinian state, while 36 percent are opposed.
Respondents in the poll were split on whether the next president should keep ObamaCare, with 49 percent in favor of keeping it and 45 percent in favor of a repeal.
Democrats and Republicans polled were nearly flipped on their views, with 80 percent of Democrats saying the law should be kept, while 82 percent of Republicans saying it should be repealed.
ObamaCare faces a challenge in coming months as the Supreme Court decides whether the federal government can provide tax subsidies in states that haven't set up exchanges.
The poll found a majority of Americans, 51 percent, support a pathway to citizenship, while 45 percent are opposed to such a plan, which has been a top issue since Obama's executive action in November.
As voters favoring a pathway to citizenship look to 2016, 55 percent in the poll said it was "very" or "extremely" important to elect someone someone who shared their view.
Forty-five percent in the poll opposed a pathway to citizenship.
The poll of 1,003 adults was conducted March 26-29 via landlines and cellphones with a margin of error of 3.5 points.
- Updated at 2:03 p.m.