That's because the U.S. military's support for the Saudi-led coalition's almost four-year war against Houthi rebels in Yemen is already limited.
In early November, Saudi Arabia and the Pentagon announced an end to the U.S. midair refueling mission to the coalition's warplanes fighting in Yemen.
Underway since shortly after the Saudis and other Gulf countries sent troops into Yemen in March 2015 to put down a Houthi-led revolt, the refueling mission had been the largest visible U.S. military assistance to the Saudi coalition. But the refueling mission had grown increasingly controversial as the number of civilian casualties associated with the coalition's airstrikes in Yemen kept rising.
In early November, Saudi Arabia announced it no longer needed the American refuelings because they had increased their own military capabilities. Defense Secretary James Mattis supported the move noting that perhaps only 13 to 15 percent of Saudi coalition missions involved American refueling.
On Thursday, the Pentagon acknowledged that accounting errors had resulted in the U.S. undercharging Saudi Arabia and the United Arab Emirates by $331 million for the reimbursement cost of the refueling mission.
The other facets of U.S. military assistance in Yemen are smaller, though significant.
The U.S. still provides intelligence and reconnaissance to Saudi Arabia and the United Arab Emirates in their fight against the Houthis.
And a small U.S. military team in Riyadh, Saudi Arabia provides guidance to the Saudi military to carry out airstrikes in Yemen that minimize the potential of civilian casualties. That includes identifying "no fire" or "restricted" sites like hospitals, schools or mosques that help military planners determine when an airstrike could result in civilian casualties.
Mattis has praised that effort as helping to reduce the number of civilian casualties in planned airstrikes, but noted that more work needs to be done with dynamic targeting, “where they’re under fire or taking fire, and they’re calling in air support."
The Senate resolution would not have impacted the U.S. counterterrorism mission in Yemen against al-Qaeda in the Arabian Peninsula and the Islamic State.
The U.S. does not have any U.S. forces in Yemen as part of this mission, which is primarily conducted by drone aircraft to target enemy fighters.
However, in recent years small numbers of special operations teams have been sent to Yemen to carry out intelligence missions or to launch raids on terrorist leaders.