UPDATE 1-Medicare dispute clouds Obama's Treasury pick -Republican senator

WASHINGTON, Feb 7 (Reuters) - Republican U.S. Senator Jeff Sessions on Thursday warned that President Barack Obama's nominee for Treasury secretary could face a tough time winning confirmation if the White House did not clear up a dispute over the Medicare health program.

Jack Lew, Obama's former chief of staff and budget director, is due to testify on Wednesday before a Senate panel that is vetting him for the administration's top economic job. Lew would succeed Timothy Geithner who left office last month.

Republicans say that a 2003 Medicare modernization law requires the administration to submit a proposal to Congress to fix a financial shortfall in the government-run health program for retirees if Medicare trustees issue a funding warning.

"In order to properly consider Mr. Lew's nomination, Congress will need documents pertaining to his role in the violation of this law, as well as a concrete legislative proposal that brings the administration into legal compliance," Sessions said in a letter to acting White House budget director Jeffrey Zients.

Sessions, the top Republican on the Senate Budget Committee, said that "failure to do so could make it difficult" for Lew's nomination to move forward. The Alabama senator did not elaborate, and his office did not comment when asked if Sessions would to try to block the nomination.

Although Democrats control the Senate 53-45, Lew may need as many as 60 votes to win confirmation if any senator seeks to block his nomination procedurally. Sessions is one of two Republicans to have publicly signaled opposition to Lew's nomination. Bernie Sanders, an independent who caucuses with the Democrats, has said he would not support Lew for the job.

In June 2011, more than 40 Republican lawmakers sent Obama a letter urging the White House to submit its Medicare legislative proposal. Many of them sit on the Senate Finance Committee, which is in charge of vetting Lew for Treasury secretary.

When asked for comment on Thursday, the White House noted that former President George W. Bush said in a 2003 statement that the provision was non-binding.

"The executive branch considers the requirement to submit legislation in response to the Medicare funding warning to be advisory and not binding," Zients said in a Feb. 5 letter to Sessions.