The bridge fell Thursday after a truck carrying an oversize load struck one of its beams. The collapse caused two vehicles to fall into the river's icy water and cut off a key link in truck and tourism traffic between the United States and Canada.
Three people were pulled from the water and treated for minor injuries.
Travis Phelps, a spokesman for the state Department of Transportation, said "it could be weeks" before the bridge is repaired.
"This is going to be a long-term traffic issue, because we need to rebuild this section of the I-5," he said.
Inslee -- appearing at a news conference with U.S. Sens. Patty Murray and Maria Cantwell and U.S. Rep. Suzan DelBene -- said Friday officials were considering whether a portable structure known as a Bailey Bridge could be used as a stopgap until a permanent fix is found, The Seattle Times reported.
He said replacing the bridge with a new permanent span could cost as much as $15 million, but the state will "restore this artery of commerce and economic growth" as quickly as possible.
The bridge normally carries an average of 70,000 vehicles per day, 12 percent of which are trucks, the newspaper said.
The bridge, now lying in the river, was built in 1955. It was inspected twice last year and appropriate repairs were made, state Transportation Secretary Lynn Peterson said.
It is classified as a "fracture critical" bridge in the National Bridge inventory, which indicates the failure of a singular structural part could wreck the entire bridge.
The Washington state Department of Transportation confirmed a statement by the company that operates the truck that struck the bridge that said it had a permit from the state to carry an oversize load on the bridge.
The driver of the truck, identified as William Scott, of Spruce Grove, Alberta, voluntarily provided investigators with a blood sample for an alcohol test and was not arrested, the newspaper said.