Senate leaders reached a deal late Thursday to confirm three more of President Obama's nominees to top government positions, but delayed a vote until January to confirm the next chairman of the U.S. Federal Reserve.

Alejandro Mayorkas, nominated to serve as deputy secretary of homeland security. (AP)

With the start of a two-week recess fast-approaching, the agreement appeared to ease more than a week of tension between Democrats and Republicans over the confirmation of several picks to lead federal agencies and serve on federal courts following changes to how the Senate confirms most nominees.

Senators planned to complete work late Thursday on the annual defense policy bill and meet again Friday morning to confirm Alejandro Mayorkas to serve as deputy secretary of the Department of Homeland Security; John Koskinen to lead the Internal Revenue Service; and Brian Davis, to serve as federal district court judge in Florida. Davis has waited more than 650 days for a confirmation vote.

Mayorkas, currently the director of U.S. Citizenship and Immigration Services (USCIS), has faced GOP opposition amid scrutiny by a DHS watchdog over allegations that he mismanaged a visa program for foreign investors.

But Senate Majority Leader Harry M. Reid (D-Nev.) and fellow Democrats insisted that Mayorkas should be confirmed,because DHS -- the government's third-largest agency -- has been without permanent leadership for several months. Senators last week confirmed Jeh C. Johnson to serve as the next secretary of homeland security, but deputy secretaries traditionally handle day-to-day management duties.

Eager to make use of new rules that only require a majority of senators to agree to end debate on a nominee, Reid has devoted most of the Senate calendar this month to confirming dozens of Obama's picks for lower-level government positions. But Republicans furious with the changes have insisted on prolonging debate on each nominee by refusing to yield back hours of time set aside to debate each nominee. That decision has forced senators to take votes in the middle of the night and early in the morning and threatened to keep the Senate open through Saturday evening.

But by Thursday night, senators appeared eager to leave town to enjoy their first extended Christmas break in at least five years.

"I think the solution to this is not to throw daggers at each other but to sit down and talk this through," Sen. Dan Coats (R-Ind.) said on the Senate floor shortly after the agreement was announced.

As part of the agreement reached late Thursday, senators will vote to end formal debate on the nomination of Janet Yellen to lead the Federal Reserve, but not confirm her until they return on Jan. 6.