Scalise was shot at a congressional baseball practice just outside of Washington.
According to Abby Livingston with The Texas Tribune, Rep. Kevin Brady and Rep. Mike Conaway have been reported safe.
The staff member, Zack Barth, posted on Facebook that he was shot and is at the hospital but is "okay".
Barth, from the Houston area and an alum of UT Austin, is a legislative correspondent in Williams' office.
The president tweeted Wednesday, "Rep. Steve Scalise of Louisiana, a true friend and patriot, was badly injured but will fully recover".
Scalise was hit in the hip and is expected to survive. "Thank you to Capitol Police for your heroism and service". The assailant has been identified as James T. Hodgkinson.
In a statement, Barton said that shortly after 7 a.m.
Please keep the member of my staff and all members of the congressional baseball team in your thoughts in prayers during this extremely hard time. Capitol police officers returned fire in an exchange that lasted around 10 minutes.
At a mid-morning press conference, law enforcement officials said it was too early to comment on a number of aspects of the shooting, including whether the lawmakers were targeted.
Four Texas congressmen who were practicing for tomorrow's congressional baseball game, an annual tradition between Democrats and Republicans, are confirmed to be safe.
"We are all Americans, and we must stand together against any attempt to divide us", U.S. Rep. Several committee hearings were postponed. Kay Granger, R- Fort Worth, said in a statement.