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The Kentucky Republican, who plans to step down as Senate minority leader at the end of the year, had blamed the former president’s lies about the 2020 election for the Jan. 6 riot.

The long-serving Republican leader said he would step aside from the role at the end of his term but remain in the Senate, acknowledging that his views on national security had put him out of step with his party.

The minority leader’s handling of the border and foreign aid legislation drew scorching criticism from far-right Republicans, though he scored a legislative win on an issue he regards as existential and part of his legacy.

Party leaders, national security institutionalists and centrists made up the core of the 22 Republicans who joined Democrats in pushing through the military aid, defying former President Donald J. Trump.

The minority leader privately told Republicans that the former president had put his party “in a quandary,” casting further doubt on the deal’s chances and the fate of Ukraine aid that the G.O.P. has tied to it.

A dozen hard-line Republicans ground business to a halt in protest of the deal Speaker Mike Johnson struck with Democrats to avert a shutdown, leaving the funding package in limbo.