The legislation is up in the air with only three days left to act before the August recess.
The Senate could vote Wednesday on the legislation.
Senate Majority Leader Harry Reid (D-Nev.) blocked Republicans from offering amendments to a bill that would end tax breaks for companies that send jobs overseas.
Sen. Jeff Sessions (R-Ala.) demanded the “essential precondition” that any bill passed to deal with the influx of immigrant children include language prohibiting President Obama from issuing more executive actions on immigration laws.
Sen. Mark Kirk (R-Ill.) introduced a bill Thursday that would require the administration to ensure that funds made available to Iran through sanction relief aren't used to support terrorism.
Senate Minority Leader Mitch McConnell (R-Ky.) said he wants a vote on his Save Coal Jobs Act as an amendment to a bill that would end tax breaks for companies that send jobs overseas.
In addition to the border money, the bill contains $615 million to combat wildfires.
Sen. Orrin Hatch (R-Utah) said Democrats' claims that there is a tax loophole for U.S. businesses that ship jobs overseas are false.
The Senate voted 93-7 on Wednesday to advance a bill that would end tax breaks for companies that send jobs overseas.
Senate Majority Leader Harry Reid (D-Nev.) said if Walgreens decided to move its headquarters to Switzerland it would be the definition of “exploitation.”