Senator Lindsey Graham , who is close to Trump, said a limited re-opening of a few weeks would allow talks to resume between Republicans and Democrats.
The partial government shutdown has now become the longest in US history.
It has left hundreds of thousands of public workers unpaid and government offices closed.
President Trump is refusing to approve a budget unless it includes $5.7bn for a wall along the Mexican border.
Democrats have rejected his request and say they will not negotiate further until the government is reopened.