Scalia's death two weeks ago has rocked the U.S. political scene. Without Scalia, the court now has four conservative and four liberal justices, meaning that any potential Obama nominee could tip the balance of the court to the left for the first time in decades.
The Republican lawmakers said last week that they plan to reinforce their position at the White House meeting to wait until after the election to fill the vacancy.
"We look forward to reiterating to him directly that the American people will be heard and the next Supreme Court justice will be determined once the elections are complete and the next president has been sworn into office," the pair said in a statement.
Senate Democratic Leader Harry Reid and the top Democrat on the Judiciary committee, Patrick Leahy, will also attend the White House meeting.