Sen. Ted Cruz, a leading voice in the national debate over immigration, on Monday appeared before a group that supports curbing both illegal and legal immigration and urged his fellow Republicans in the House to reject immigration reforms approved earlier by the Senate.

Cruz, the son of a legal immigrant from Cuba, has not publicly called for limits on legal immigration and made he no mention of such restrictions in his address to the DC March for Jobs outside the Capitol. But March organizers — including the Black American Leadership Alliance and Tea Party groups — do support curbing legal immigration, saying it could take jobs away from “millions of American citizens.” Cruz also claimed the Senate immigration reform would cost Americans’ jobs but without specific reference to legal immigrants.

“If this bill is passed, it will increase unemployment,” Cruz, R-Texas, said. “If this bill is passed it will increase African American unemployment. If this bill is passed it will increase youth unemployment. If this bill is passed it will increase Hispanic unemployment.”

House leaders insist they have no intention of taking up the Senate bill, which provides a pathway to citizenship. And many House Republicans, like Cruz, cite a similar approach taken in 1986 that allowed undocumented workers to be legalized but lacked the border security measures needed to prevent millions of other illegal immigration from crossing a porous border.

“We might have been foolish enough to fall for this once in 1986,” Cruz said, “but we’re not foolish enough to fall for it again.”

Cruz argued that border security should be the focus of reform efforts, citing the elevated threats the U.S. has faced following the Sept. 11, 2001 terrorist attacks.

“We’ve got to get serious about securing our borders,” said Cruz as members of the audience waved flags from his home state of Texas. “It doesn’t make any sense, especially in a post-9/11 world, that we don’t know who is coming into this country.”

The March for Jobs started at Freedom Plaza under a sweltering July sun and made its way to the north side of the Capitol, and included activists from across the country. Also on hand was former Rep. Allen West, a Tea Party favorite who many in the audience were urging to run for president, and Rep. Steve King, one of the House’s most outspoken critics of the reform attempts.

King, R-Iowa, said proponents of immigration reform include “elitists who want cheap labor to clean their houses and mow their lawn,” business leaders who want to keep wages low and Democrats looking for more voters.

“You don’t sacrifice the rule of law,” King said, “so you can have undocumented Democrats.”