Trump was in Corpus Christi, Texas, on Wednesday to meet with officials.
House GOP leaders have signaled they are aiming to act fast on Harvey aid and a vote is likely next week.
Trump plans to return to Texas on Saturday to assess more of the flood damage and later plans to visit Louisiana. Much larger future installments will be required but the initial package, to replenish Federal Emergency Management Agency disaster coffers through September 30, shouldn't be controversial.
Mr. Trump, along with Pence, led a second meeting with his Cabinet and senior members of the administration on Sunday to discuss the federal response and recovery efforts to Hurricane Harvey.
But the New York Times said that while he has "a chance to reclaim the presidential high ground...many of those in the president's orbit are anxious Mr. Trump will not be self-controlled enough to maximize the moment".
He also says no routine sweeps will be conducted in emergency shelters.
Sanders said the president will accept suggestions from the media and the public about which organizations to support.
Hurricane Harvey has been labelled one of the most powerful storms to hit the United States in a decade.