An influential bipartisan duo of lawmakers is using this week’s consideration of a must-pass defense spending bill to try to help millions of people in Yemen, where a Saudi-led, U.S.-backed coalition has killed thousands of civilians in a conflict that has created desperate new health and starvation crises.

Sens. Todd Young (R-Ind.) and Chris Murphy (D-Conn.) are rallying support for an amendment to the 2018 National Defense Authorization Act that would condition U.S. military support for Saudi Arabia on American officials guaranteeing that Riyadh is following international humanitarian law, particularly on permitting the delivery of American-bought cranes to unload ships filled with food at a major Yemeni port.

But it remains unclear whether the Young-Murphy proposal will receive a vote on the Senate floor. That depends on two factors: how many lawmakers agree privately to support the idea if it is debated, which makes it more likely that the original co-sponsors will push hard for it; and how Sen. John McCain (R-Ariz.), who leads the legislative process on the defense bill as chair of the Senate Armed Services Committee, and Senate Majority Leader Sen. Mitch McConnell (R-Ky.) react when pushed on the question of presenting the amendment.

It remains an uphill battle.

The Trump administration and many lawmakers, particularly those in the GOP, agree with the sentiments of Senate Foreign Relations Committee chairman Sen. Bob Corker (R-Tenn.), who this week reiterated that he does not believe arms sales should be conditioned on human rights worries. (U.S. strategic concerns are of course another matter: Corker has put his own hold on approving weapons sales to Saudi Arabia and its coalition partners Bahrain and the United Arab Emirates until they resolve a dispute with fellow U.S. partner nation Qatar.)

But the new bipartisan proposal of such a striking measure ― one that specifically targets ― shows how angry lawmakers have become about the coalition’s humanitarian impact on the Middle East’s poorest country.

Capitol Hill conversations about Yemen that used to focus primarily on the impact of U.S.-supported airstrikes now broadly cover the general devastation of the nation, which is also facing an unprecedented outbreak of cholera, according to Kate Gould of the anti-war advocacy group Friends Committee on National Legislation.

Even members of Congress sympathetic to the Saudis’ arguments, especially the claim that they must be assertive in the region to counter Iran, now seem ready to pressure the coalition over its airstrikes. Known hawk Sen. Marco Rubio (R-Fla.) has, through McCain, submitted an amendment to require new U.S. government reporting on how the war is being conducted ― a tacit acknowledgement of repeated allegations that the coalition is hitting civilian targets like funerals and hospitals, perhaps even on purpose.

Coalition airstrikes have hit civilians five times, killing more than 100, since the Senate last considered the war during a June 2017 vote on whether to sell Saudi Arabia precision-guided bombs, according to research from the advocacy group Yemen Peace Project.

Supporters of the kingdom say the transfer of those munitions is one way to help reduce civilian casualties in the conflict between the coalition and Iran-allied Yemeni Houthi rebels. For its part, Saudi Arabia has for months said they are working to improve targeting and investigating all claims of hitting civilians.

The coalition’s delay of humanitarian relief shipments ― which it says is necessary because of weapons smuggling concerns ― has hurt millions of Yemenis, prompting World Food Program chief David Beasley to declare earlier this month that he believes Saudi Arabia should pay for all humanitarian assistance to Yemen.

Beasley’s organization asked the Saudi government about the U.S. cranes earlier this summer and he later said they received no response. The issue has become a particular focus for Sen. Young, who accuses the Saudi-led coalition of preventing aid from reaching areas controlled by the Houthis it is fighting.

“Saudi Arabia is an important regional security partner, but we cannot ignore when our partners use food or medicine as weapons of war,” Young told HuffPost in a Wednesday email. “The actions of the Saudis in Yemen undercut our national security interests and our moral values—exacerbating the world’s largest humanitarian crisis.”

Young has repeatedly highlighted the Saudis’ actions, which he says boost the risk of extremist recruitment by Al-Qaeda, the self-described Islamic State and other anti-U.S. military groups in Yemen.

He has provided a mainstream GOP counter-balance to Sen. Murphy, one of few other lawmakers to regularly draw attention to the Yemen crisis. (The other Republicans often vocal about the war, Sens. Rand Paul (Ky.) and Mike Lee (Utah), are seen as fringe figures in their party on foreign policy and unlikely to win over more GOP support.)

By Wednesday, activists trying to secure guarantees of support for the Young-Murphy proposal said the situation remained unclear but they remain hopeful.

“More and more [lawmakers] are starting to question blank check support of the coalition, and while it’s unclear how much support this specific amendment would get, more and more offices, especially on the Republican side of the aisle, are open to having the conversation,” said Kate Kizer of the Yemen Peace Project.

They pledged to continue lobbying senators, noting that getting the amendment to the floor could indicate progress following a previous win over the summer, when critics of the war convinced 47 senators (including almost the entire Democratic caucus) to vote against the precision-guided munitions deal.

A similar effort a few months earlier to block a transfer of tanks received support from only 27 senators.

“It’s a real opportunity to build on the momentum,” Gould said.

Human rights organizations like Oxfam America are trying direct appeals to constituents over the amendment.

Raise your voice now and tell your Senators that you support Senator Young's amendment to protect people in Yemen! Call 1-866-374-0409 now. pic.twitter.com/kzfSk0sIop — Oxfam America (@OxfamAmerica) September 12, 2017

And the establishment support of Rubio’s proposal for new American oversight of support for the coalition has already buoyed the war’s critics.

“It’s a small win for transparency,” Kizer said. “It’ll be the first [Pentagon] assessment of Saudi performance in the war.”

Outrage over the conflict continues to grow beyond Washington.

Activist organizations focused on the Yemen conflict like the International Campaign for Freedom in the United Arab Emirates participated in major protests at the world’s largest arms fair earlier this month. And the United Nations High Commissioner on Human Rights on Wednesday won support from China, a powerful member of the U.N. Security Council, in an effort to set up an independent inquiry to investigate alleged war crimes by both the Saudi-led coalition and the Houthis in Yemen.

The U.S. and Saudi Arabia oppose the idea of the inquiry.

UPDATE: Sept. 14 ― Young and Murphy on Thursday afternoon filed their amendment , which would prevent U.S. aerial refueling for Saudi aircraft pending American certification that the Saudis are following international humanitarian law. In a sign that the lawmakers’ behind-the-scenes work was paying off, the two gained an additional mainstream GOP co-sponsor, Nevada Sen. Dean Heller. But the chances of a vote remained unclear. Earlier in the day, McCain and McConnell suggested that perhaps no amendments would receive votes. Negotiations are ongoing.

CORRECTION: An earlier version of this article stated that McCain endorsed Rubio’s amendment. In fact, McCain only submitted the amendment on Rubio’s behalf. He has not formally endorsed it.