Sen. Lindsey Graham of South Carolina put the onus on the Obama administration Tuesday to put together a proposal for comprehensive immigration reform, “and see if they can sell it” to skittish lawmakers.

Only days before thousands of immigration overhaul advocates are expected to descend on the Capitol for a March 21 rally, Graham, the sole Republican involved in efforts to draft a Senate bill, suggested it was up to the White House to release a proposal first.

His remarks seemed calculated to ratchet up the pressure on the president, against the backdrop of growing frustration by advocates of an immigration overhaul. Obama met March 11 with several Hispanic lawmakers and representatives of immigration groups, after which he released a statement, saying that “my commitment to comprehensive [immigration] reform is unwavering.”

In an interview Tuesday, Graham deflected calls for action from the Senate Judiciary Committee, where he and Charles E. Schumer, D-N.Y., have been working on a bipartisan plan for months but have yet to release something. Instead, he directed attention to the president.

“To demonstrate that commitment, he ought to put a bill together,” he said.

Graham said Tuesday that he and Schumer intend to “do an op-ed piece soon to lay out a way forward,” to be published this week, though he declined to offer specifics.

While Schumer has expressed optimism about a legislative path forward, Graham has been more circumspect.

“Using reconciliation on health care is going to make it hard to do anything,” he repeated Tuesday, echoing a warning he first made last week during a meeting with Obama and Schumer at the White House.