WASHINGTON — Senate Republicans will move this week to speed the confirmation of President Trump’s cabinet, an effort that has been stymied by the combination of lax preparation by Mr. Trump’s transition team, his many unorthodox nominees and Democrats spoiling for a fight, albeit with few cards in their deck.

On Monday, the Senate will vote on the confirmation of Representative Mike Pompeo of Kansas to lead the Central Intelligence Agency, after Democrats used one of the few procedural maneuvers left to them to force a debate on his inevitable approval.

Republicans had hoped to push through Mr. Pompeo and others last Friday, but were able to confirm only two: James N. Mattis for defense secretary and John F. Kelly to lead homeland security. President Obama had seven nominees approved on his first day in office.

Also on Monday, the Senate Foreign Relations Committee will vote on Mr. Trump’s pick for secretary of state, Rex W. Tillerson, whose road to confirmation has been bumpy. Mr. Tillerson received a lift on Sunday when two Republicans, Senator John McCain of Arizona and Senator Lindsey Graham of South Carolina, said they would support him, after weeks of public hedging.