Republicans have accused Obama of remaining in perpetual campaign mode rather than working with lawmakers to reach a deficit-reduction deal.
The administration says Republicans are holding up the process by refusing to place revenues on the table or acknowledge Obama's past efforts to curb deficit growth.
Alexander is the leading Republican on the Senate Health, Education, Labor and Pensions (HELP) Committee.
On Tuesday, he decried Obama as unserious about federal spending cuts.
"My hope is that President Obama steps back and thinks about his second term and realized that he is a talented president … [but] that he has a major challenge facing him" on entitlements, Alexander said.
"We are only one budget agreement away from getting the country moving again and reminding the world of our global preeminence," he said.