"We are not going to impeach people because we have disagreements," said Graham.
The Republican senator also invited the president's personal lawyer Rudy Giuliani to tell the Senate Judiciary Committee about his findings and answer questions about his own conduct.
The House of Representatives on Wednesday held a marathon debate ahead of planned votes on two articles of impeachment accusing the president of abusing his power and obstructing Congress.
Separate votes are expected in the early evening.
The votes are expected to fall almost entirely along party lines, with Democrats in favor and Republicans opposed.
The articles are expected to pass the Democratic-controlled chamber and make Trump only the third U.S. president to be impeached.