Needing 60 votes to advance, the motion fell 50-46.
Democrats called the amendment from Sen. Tom Cotton of Arkansas a "poison pill" added at the last minute to an otherwise bipartisan $37.5 billion funding bill for the Energy Department and other agencies and said GOP leaders must take steps to shed it or the important spending bill would be lost.
"The onus is on them and we're not going move forward until this do this," said Sen. Chuck Schumer of New York, a top Democratic leader. "This is totally extraneous and at the last minute."
Republicans defended Cotton's right to offer the amendment and accused Democrats of purposely derailing the bill to prevent the GOP-led Senate from getting another in a series of recent bipartisan accomplishments passed on the floor.
"Yet another way to blow up the appropriations process," said Senate Majority Leader Mitch McConnell after the vote. "No matter what the issue, there is a new and creative way to throw a monkey wrench into the gears."
He said it was "ridiculous" for the Senate to be stalled like this.
Democrats denied that was their intent and argued the opposite was true: They were trying to preserve the bill that faced a veto threat from President Barack Obama if the Cotton amendment was included.
The White House said it was "gratified" that the amendment wasn't moving forward. "I'd say that we're gratified that this is not advanced in the Senate," said spokesman Josh Earnest, who then dismissed Cotton's nuclear expertise.
"I'm confident that he couldn't differentiate heavy water from sparkling water," Earnest said.
Earnest said the amendment was part of Cotton's "repeated commitment to undermining the successful implementation" of the nuclear deal with Iran. "We've made clear our commitment to a principle that ideologically motivated policy writers are not appropriate for appropriations bills," Earnest said.
Republicans have sharply criticized an administration plan that came to light last week to buy from Iran 32 metric tons of heavy water, which is a key component in nuclear reactors. Republicans complained it was another bad byproduct of the nuclear accord with Iran that amounted to the U.S. directly subsidizing Iran's nuclear program.
Democrats argued there are better ways for Cotton to address his concerns with the heavy water arrangement without disrupting the appropriations process, which senators on both sides of the aisle are trying to restore after years of gridlock and dysfunction.
"Maybe he's a new member," said Sen. Dianne Feinstein of California, the top Democrat managing the bill. "Why can't he wait for another time. I've been here 24 years. I waited for another time plenty of times because somebody said your amendment won't go well with the bill."
Cotton said his amendment was filed late because the heavy water purchase was learned about only Friday. He also offered to have his amendment face a supermajority threshold for passage -- not a simple majority vote that Senate rules would dictate for an amendment like this -- but Democrats rejected that offer.
Republicans charged that Democratic leaders and the White House are opposed to holding a vote because they fear many Democrats will support Cotton's ban, something that could be an embarrassment to the President.
Speaking on the floor, Cotton sounded conciliatory saying he is "committed to working in good faith" to try "to reach some solution, whether on this bill or another" to prevent U.S. payments to Iran while also allowing the appropriations bills to pass.
Just over a year ago, Cotton made headlines when he spearheaded an open letter to Iran signed by 47 Senate Republicans that said future U.S. presidents might overturn any deal Obama reached related to Iran's nuclear program.
After the vote, McConnell took procedural steps that would allow a revote to break the Democrats' filibuster if a deal is worked out. And Sen. Lamar Alexander of Tennessee, the top Republican on the bill, held out hope that a deal could be reached on Cotton's amendment soon.
"Let see if we can't work it out. I'd like to do that," Alexander said.