Vitter's amendment would end the ability of the White House to appoint policy "czars," and prohibit funds for salaries and expenses for appointed czars. DeMint's would strike language in the bill that eliminates the need for Senate confirmation of nominees for the position of director, Bureau of Justice Statistics.

Senate Majority Leader Harry ReidHarry ReidIf Gorsuch pick leads to 'crisis,' Dems should look in mirror first Senate confirms Mulvaney to be Trump’s budget chief Democrats declare victory after Puzder bows out MORE (D-Nev.) indicated that Thursday's schedule could include more votes by the afternoon.

The Senate adjourned at around 7:30 p.m. Wednesday. Morning business will begin at around 10 a.m. Thursday.

-- This story was updated at 8:48 a.m. Thursday to correct information about DeMint's amendment.