Trump said Tuesday at California's Marine Corps Air Station Miramar that the nation's military had been "asked to do more with less" for too long.
Trump on Tuesday inspected prototypes on display in California for his "big, handsome border wall".
Gov. Jerry Brown sent a letter to Trump Monday, telling him that "California thrives because we welcome immigrants and innovators from across the globe".
Trump also slammed Brown for high state taxes, saying Brown "has done a very poor job running California".
Building a wall along the border with Mexico was a central campaign issue for Trump, who said the wall will help fight drug trafficking and unauthorized immigration.
"Without a wall there would be bedlam, I imagine", he added.
"There are certain areas where they are really wanting us to build a wall because people are complaining, people are pouring in".
But James Schwab, who quit his job as regional spokesman for the US Immigration and Customs Enforcement department, said he believed the number was much lower. "No wall!" near the San Ysidro border crossing, where tens of thousands of people enter the United States daily from Tijuana, Mexico - many on their way to work or school in San Diego.
San Diego Mayor Kevin Faulconer - who is not expected to meet with Trump during his visit - did not support a 2017 city resolution formally opposing the border, but he also did not veto it.
Official details of Trump's first visit to California since being elected have been scant.
"We know the Trump administration is full of liars".
In some brief remarks to reporters, Trump painted a curious picture of Mexican immigrants looking to cross the border.
Congress has yet to approve the funding amid skepticism and Democratic opposition, but an administration official said the wall would save far more money than it cost. The president says the state's sanctuary policies are putting the country at risk. "The criminals take refuge in these sanctuary cities".
Trump tweeted about California's immigration policies as he flew to the state aboard Air Force One. He is scheduled to arrive at Los Angeles International Airport at 3:30 p.m.in advance of a Republican National Committee fundraiser.
At the protest, passersby such as José Gonzalez, 21, stopped to snap a photo of people holding signs, including one that read: "Wall off Putin!"
Ahead of his arrival, the president tweeted that "thousands of unsafe, violent criminal aliens are released" as a result of California's immigration sanctuary policies. We must enforce our laws & protect our people!
"This is an environmental catastrophe, on top of a misallocation of government resources that could be used for health care or social services", Cody Petterson, president of the San Diego County Democrats for Environmental Action, said of the wall.
FACTS: Construction of 14 miles (23 kilometers) of imposing border walls by the mid-2000s - along with more agents, technology and smaller barriers going back to the 1990s - brought a 95 percent decline in border arrests in the Border Patrol's San Diego sector from 1993 to 2017.