The row hinges on whether the attorneys were sacked for political motives.
Democratic leaders say they could go to court to challenge Mr Bush's move. He invoked the same little-used power last month to withhold subpoenaed documents.
The White House says Mr Bush is acting in good faith and has offered to let the aides do off-the-record interviews.
The pair in question are Harriet Miers, former White House counsel, and Sara Taylor, former political director for the White House.
Ms Miers has been summoned to appear under oath before the Senate Judiciary Committee on Wednesday and Ms Taylor to testify before the House Judiciary Committee the next day.
The Democratic heads of the two judiciary committees had set a deadline of Monday for the White House to explain the first invocation of privilege last month and to log what documents were being withheld.
In a letter to congressional leaders, White House counsel Fred Fielding said their demands were "unreasonable" because they represented "a substantial incursion into presidential prerogatives".
John Conyers, chairman of the House Judiciary Committee, responded with a warning that Congress was prepared to go to court over the matter.
"Contrary to what the White House may believe, it is Congress and the courts that will decide whether an invocation of executive privilege is valid, not the White House unilaterally," he wrote. --source: BBC--