"The president promised to pass an immigration reform bill in his first year. They've done almost nothing in the White House on immigration," Graham said Sunday on NBC's "Meet The Press."
The White House has suggested Graham and Sen. Sen. Chuck Schumer, D-N.Y., write reform legislation for Obama to consider, Politico reported Sunday.
But Graham said the president should draft the legislation.
"I urge the president to write a bill and see if he can get another Republican, see if he can convince the 16 Democrats who voted no (on reform) last time," Graham said.
"Let him do some heavy lifting here on immigration....Write a bill and send it to me. I'll be glad to look at it."
But Schumer, also appearing on "Meet the Press," said Graham had understated Obama's commitment to immigration reform.
"The president supported our framework and he'll be right up front in helping us," Schumer said.