By vote of 56-42, Republican-majority Senate falls short of 60 votes needed in the 100-member chamber to advance the legislation.
Joseph Lieberman will be the new chairman of the United Against Nuclear Iran organization.
98-1 vote sends measure to US House of Representatives, which is expected to consider it as soon as next week.
"Our priority is to make sure the bill gets passed with the strongest possible bipartisan majority so that Congress is guaranteed the opportunity to pass judgment on the final agreement," an AIPAC source said.
White House supports revisions; Democrats hail bill as a demonstration of compromise; Republicans say bill provides Congress "very little teeth" by way of oversight.
Full committee to review compromise that would shorten Congress' review to 52 days of any final deal on Iran's nuclear program.
Senate Foreign Relations Committee is scheduled to debate and vote on Tuesday afternoon on the measure put forward by Senator Bob Corker.
A number of leading US senators remain unswayed following months of intense and controversial Israeli efforts to block a nuclear deal with Iran.
Cruz receives extended applause after criticizing Obama's relationship with Israel.
Senator takes overt swipes at senior administration officials involved in negotiations.