BUTTE, Mont.—It was a family Fourth of July for Democrat Barack Obama as his wife, daughters, sister and other relatives helped him make an Independence Day play for this reliably conservative state.

Obama paid tribute to a nation in which the son of a single mother could rise to such heights.

“I know that there is no other country out there where I could be standing before you as somebody who could potentially be president of the United States,” he said at a campaign-sponsored “family picnic” for hundreds of people—part rally, part birthday party for his oldest daughter, Malia, who turned 10 on Friday. “We are going to change the world.”

Cheers greeted Obama, his wife, Michelle, and their two daughters everywhere. As they arrived to watch the Fourth of July parade, the crowd broke into a rendition of “Happy Birthday” for Malia.

Obama joked that he had to tell the birthday girl not to get caught up in all the fuss.

“All the fireworks and stuff are not just for her,” he said to laughs.

That appeared in part a reference to the special treat the family got Thursday night. Obama’s motorcade ferried the family from their private jet to a home high above town that provided a stunning view of the city’s late-night fireworks display.

Friday’s picnic was held on a sunny, green hillside, a mountain vista all around, with checkered tablecloths and plenty of food dotting the property of the World Mining Museum.

Introducing her husband, Michelle Obama spent almost more time talking about all the relatives who were there than “the other guy” running for president. She led the crowd in another round of “Happy Birthday,” then noted that mom singing into a microphone might not be the best present for a young girl.

“Now, she’s thoroughly embarrassed,” she laughed.

Continuing the theme of focusing on children, Michelle Obama said “those little people and all the beautiful kids all over this park” are driving him to run for president no matter the sacrifice it costs their family.

“The reason why I am standing here today is that if he cares half as much about this country as he does about his own children, we’re going to be just fine,” she said.

The Obamas spent part of the afternoon sitting for interviews with such family friendly magazines as People, Essence and Parents, and television’s “Access Hollywood.”At the parade, Obama sat in a small riser to watch the floats. He was surrounded by his wife, daughters dressed in combinations of red, white and blue, and his sister, her husband and their daughter.

Only two Democratic presidential candidates have carried Montana and its three electoral votes since 1948.

But Obama has visited four times now—twice to the rough-and-tumble mining town of Butte. The area is the state’s Democratic and union stronghold—so Democratic that a parade float dedicated to local Republican officeholders drew complete silence from the otherwise boisterous crowd.

Obama’s Republican rival, John McCain, was spending the long holiday weekend at home in Phoenix.