Hoping to persuade lawmakers to provide immunity for telecom companies that cooperated with its warrantless surveillance program, the White House agreed Thursday to allow members of the House Judiciary and Intelligence committees limited access to some documents surrounding the program.

By a 60-34 vote margin, the Senate defeated on Thursday afternoon a Senate Judiciary Committee bill that would have reauthorized the Foreign Intelligence Surveillance Act without retroactive immunity for telecom companies. Now, the Senate may consider a Senate Intelligence Committee version that includes protection from over 40 lawsuits alleging legal violations.

FISA authority expires on Feb. 1, since Congress passed a stop-gap measure before leaving for the August recess.

House Intelligence Chairman Silvestre Reyes (D-Texas) and House Judiciary Chairman John Conyers (D-Mich.) have been demanding access to the documents for several months. Senators were given access to the material in the fall.

Now, select House lawmakers and staffers will be given security clearances to be “read-in” to the classified program.

“I have pushed for eight months to review this material,” Reyes said in a statement on Thursday. “I don’t know why the White House refused to give us access.”

But Conyers expressed disappointment with the fact that the information was not offered to the whole Judiciary Committee and that “some materials on this and other administration programs are still being withheld.”