The Senate is set to take up President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's veto of legislation cutting off U.S. support for the Saudi-led war in Yemen next week, though any override attempt is expected to fall short.

Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE's (R-Ky.) office said Thursday that the chamber would "process the president’s veto message on the Yemen resolution by the end of the week."

Trump vetoed the measure earlier this month, the second veto of his presidency. The resolution requires him to withdraw any U.S. troops in or "affecting" Yemen within 30 days unless they are fighting al Qaeda.

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Because the Senate voted first on the resolution, any override attempt will start in that chamber. Neither the Senate nor the House are expected to have the votes to overcome Trump's veto.

The Senate passed the Yemen resolution in a vote of 54-46 last month. Because supporters were using the War Powers Act, they were able to pass the resolution with only a simple majority and avoid the 60-vote filibuster that legislation normally must overcome.

McConnell did not support the resolution, and his office did not specify Thursday what action the Senate would be taking to "process" the veto message. Overriding Trump's veto would require 67 votes in the Senate.

Aside from a straight vote on overriding the resolution, there are several procedural tactics Republicans could use to try to deal with Trump's veto message.

For example, senators could try to send the resolution to committee or table it, according to the Congressional Research Service, effectively pigeonholing the veto message and squashing an override attempt.

Saudi Arabia has emerged as a growing cause of divide between Trump and Congress in the wake of the slaying last fall of Washington Post contributor Jamal Khashoggi, a U.S. resident who was a vocal critic of the Saudi government.

But frustrations on Capitol Hill with the U.S.-Saudi relationship run back years.

Senators have put a blockade on arms sales to Saudi Arabia. And the only override of a veto from former President Obama came when Congress shot down his attempt to block legislation allowing families of 9/11 victims to sue Saudi Arabia in U.S. courts.