And in Connecticut, Senator Joe Lieberman has announced he will run as an independent if he loses next month’s Democratic primary. Lieberman is in a tight race with challenger Ned Lamont. His popularity has waned among Democrats over his support for the Iraq war and other policies backed by President Bush. Lieberman’s campaign has begun collecting signatures towards putting him on the ballot as an independent in the event he loses the race. In a statement, Democratic Senator Hillary Clinton of New York said she hopes Lieberman wins the race, but will support the nominee chosen by Democratic voters. On Tuesday, Lieberman was heckled as he took part in an Independence Day Parade in his home state. One group of demonstrators carried two giant paper-mached mâché heads of Lieberman locking lips with President Bush. Lieberman dismissed the protesters, calling them “a distant minority.”