As the crowd entered the memorial plaza, they chanted "Tear down these walls" and "You work for us." They sang "God bless America" and other songs.
"Our vets have proven that they have not been timid, so we will not be timid in calling out any who would use our military, our vets, as pawns in a political game," Palin told the crowd.
The memorial has become a political symbol in the bitter fight between Democrats and Republicans over who is at fault since the shutdown began on Oct. 1. Earlier rallies have focused on allowing access for World War II veterans visiting from across the country with the Honor Flight Network.
Sunday's rally was more political. A protest by truckers converged with a rally by a group called the Million Vet March at the World War II Memorial. Participants cut the links between metal barriers at the National Park Service site and pushed them aside.
Later, some protesters carried metal barricades that look like bicycle racks from the memorial to the White House and stacked them up outside the gates, confronting police in riot gear. Some protesters carried signs reading "Impeach Obama."
Police moved the protesters back to set up barricades between the crowd and the White House gate. Some protesters chanted "shame on you" at the officers.
An armored police vehicle also was sent to the World War II Memorial as people lingered there.
District of Columbia police said the crowd was dispersing by 1 p.m., about four hours after the protests began. U.S. Park Police said there had been one arrest at the Lincoln Memorial for assault, but it was not related to the protest, said Lt. Pamela Smith.