Senate officials declined to say today when that might be.
Senate officials said they did not expect the lawmakers to return until after Thanksgiving.
Senate officials said today that there was a basic understanding on the framework for such a plan.
Senate officials have said that the population range among districts and the addition of a seat are legal.
Senate officials expect the inquiry to last at least two months, and to cost from $250,000 to $500,000.
For the last three years, Senate officials said, such costs ran to $4 million a year.
"They are going to have windfall of $33 million," the Senate official said.
Senate officials have indicated they would take no similar action if the House effort falls short.
Because of this, Senate officials said they hoped the debate could be wrapped up in a day.
Senate officials say they expect a committee recommendation around the August recess.