"We must secure our borders and enforce our laws, while also protecting against discrimination and adhering faithfully to the rule of law," Pelosi said in a statement after Bush's speech. "At the same time, we must enact immigration reform that is humane and honors our American tradition of being a nation of immigrants."
In another political dilemma for Bush, the more he embraces stiff conditions for visas and citizenship, the more he risks undercutting support among Democratic liberals for an overhaul of immigration rules.
"We're having productive conversations with members from both sides of the aisle in both houses about comprehensive reform," White House spokesman Gordon Johndroe said. "There are a number of proposals floating around and a number of discussions going on."
One new wrinkle under consideration by the White House would rewrite the law on legal immigration. Currently, family relations play a key role in obtaining visas that grant immigrants legal residency. Under proposals being discussed by Republicans in the Senate, business needs would take higher priority than family connections.
Democrats and several immigrant-advocacy groups are concerned about such proposals, as well as the other proposed conditions under which illegal immigrants could get work visas and seek citizenship.
On Saturday, about 7,000 to 10,000 people marched in downtown Los Angeles, protesting the proposals and calling for a broad amnesty for illegal immigrants.
Bush visited the border outpost of Yuma in May as part of his push for an immigration bill. On his return trip, he sought to stress progress in beefing up surveillance equipment and stemming illegal crossings in the area.
"When I landed here at the airport, the first thing I saw was an unmanned aerial vehicle," Bush said in his speech to about 350 border agents, National Guard personnel and local law enforcement officials. "It's a sophisticated piece of equipment. You can fly it from inside a truck, and you can look at people moving at night. It's the most sophisticated technology we have, and it's down here on the border to help the Border Patrol agents do their job."
Accompanied by Arizona Gov. Janet Napolitano, a Democrat, Bush was briefed on the aerial vehicle and inspected border fencing that Congress ordered last year.
"It's amazing progress that's been made," Bush said as he viewed the barrier, roads and lighting installed by U.S. Customs and Border Protection.