From the Beltway Confidential of The Washington Examiner:
Speaking about outgoing Secretary of the Interior Ken Salazar, President Obama reminded reporters that the family of the former U.S. Senator from Colorado was of Spanish descendent [sic] – dating back to the 16th century.
“His ancestors were living here before the Mayflower set sail,” Obama said. “As he explains it — and relevant, as we are working to get immigration reform passed — his family did not cross the border, the border crossed them. And that’s why, when I needed somebody to lead Interior, I didn’t have to look very far.”[Obama: Salazar’s family ‘did not cross the border, the border crossed them’ , Charlie Spiering, Washington Examiner, Feb. 6th, 2013]
The slogan "We Didn't Cross the Border, the Border Crossed Us" has been used by Hispanic activists for some time. Here Obama uses it to plug for amnesty.
The U.S. Southwest was sparsely populated when the U.S. took control of it in the 19th century. The vast majority of today's Hispanics are not descended from people living there then.
As for Ken Salazar's ancestry, his Wikipedia entry  states that he "has ancestors in the Southwestern United States dating back from the 16th century", indicating that all his 16th-century ancestors weren't from there.
What does Salazar's family history have to do with amnesty? The situation of Spanish-speakers residing in the Southwest when the U.S. took control was a special case. Some left for Mexico, most stayed and their families assimilated long ago. Their situation is really irrelevant to the status of millions of illegal aliens from Mexico currently in our country.
But most of the public doesn't closely analyze these issues, so linking the two cases may help to bamboozle some into supporting amnesty. That's why we need to be able to respond to such illogical but catchy slogans.