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And although about half (49%) say some Republican senators went too far by sending a letter to Iran's leaders warning that any agreement with the Obama administration would require Senate approval, only about one-third (39%) think the letter hurt U.S. efforts to keep Iran from developing nuclear weapons.

SEE: The complete CNN/ORC poll

Secretary of State John Kerry has been meeting with Iranian Foreign Minister Javad Zarif in Switzerland in an attempt to reach an agreement that would loosen sanctions on Iran in exchange for greater transparency around their nuclear programs.

Direct diplomatic negotiations with Iran are broadly popular, 68% favor them, while 29% oppose them. That support cuts across party lines, with 77% of Democrats, 65% of Republicans and 64% of independents in favor of diplomacy between the U.S. and Iran in an attempt to prevent Iran from developing nuclear weapons.

Negotiations were ongoing when a group of 47 Republican senators signed on to a letter to Iran's leaders, written by freshman Arkansas Sen. Tom Cotton, which stressed that any agreement the Obama administration reached with Iran would require Senate approval.

All told, 49% of Americans say the letter went too far, while 39% think it was an appropriate response to the way negotiations over Iran's nuclear program were going. Opinions on the letter were divided along partisan lines, with 67% of Democrats saying it went too far while 52% of Republicans called it appropriate. Among independents, 47% thought it went too far, 42% that it was appropriate.

READ: What if there's no Iran deal?

Just 18% of Americans think the letter helped U.S. efforts to keep Iran from developing nuclear weapons, while 32% thought it hurt those efforts. More, 44%, said the letter had no impact on the U.S. negotiations. A plurality of Republicans, 50%, said it had no impact, 24% that it helped, 21% that it hurt. Among Democrats, 44% said it had no impact, 30% that it hurt and 22% that it helped.

The possible 2016 field has been sparring over the letter, with several potential Republican candidates expressing support for it, while likely Democratic candidate Hillary Clinton tweeting that "no one considering running for commander-in-chief should be signing on."

Americans have greater confidence in President Barack Obama than the Republicans in Congress in dealing with major issues, whether those are domestic or related to foreign policy. Just about half said they have faith in Obama on major issues and major foreign policy issues, while 4-in-10 have greater confidence in the GOP. About 1-in-10 say they trust neither side on the big issues.

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Poll: Iran negotiations popular - CNN.com