WASHINGTON -- Congress plunged the nation into a partial government shutdown Tuesday as a long-running dispute over President Barack Obama's health care law stalled a temporary funding bill, forcing about 800,000 federal workers off the job and suspending most non-essential federal programs and services.The shutdown, the first since the winter of 1995-96, closed national parks, museums along the Washington Mall and the U.S. Capitol visitors center. Agencies like NASA and the Environmental Protection Agency will be all but shuttered. People classified as essential government employees -- such as air traffic controllers, Border Patrol agents and most food inspectors -- will continue to work. The health care law itself was unaffected as enrollment opened Tuesday for millions of people shopping for medical insurance. The military will be paid under legislation freshly signed by Obama, but paychecks for other federal workers will be withheld until the impasse is broken. Federal workers were told to report to their jobs for a half-day but to perform only shutdown tasks like changing email greetings and closing down agencies' Internet sites. The self-funded Postal Service will continue to operate and the government will continue to pay Social Security benefits and Medicare and Medicaid fees to doctors on time. The Senate twice on Monday rejected House-passed bills that, first, conditioned keeping the government open to delaying key portions of the 2010 "Obamacare" law that take effect Tuesday, and then delayed for a year the law's requirement that millions of people buy medical insurance. The House passed the last version again early Tuesday; Senate Majority Leader Harry Reid said the same fate awaits it when the Senate reconvenes Tuesday morning. "You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway, or just because there's a law there that you don't like," Obama said Monday, delivering a similar message in private phone calls later to Republican House Speaker John Boehner and other lawmakers. Boehner said he didn't want a government shutdown, but added the health care law "is having a devastating impact. ... Something has to be done."