WASHINGTON—President Barack Obama intends to propose a three-year freeze in spending that accounts for one-sixth of the federal budget—a move meant to quell rising concern over the deficit but whose practical impact will be muted.

To attack the $1.4 trillion deficit, the White House will propose limits on discretionary spending unrelated to the military, veterans, homeland security and international affairs, according to senior administration officials. Also untouched are big entitlement programs such as Social Security and...