Rep. Veronica Escobar (D-TX), who represents El Paso, disagreed with the president.
In the big speech, Mr. Trump pointed to El Paso as proof that walls work, saying a border fence tamed a city that used to be one of the country's most unsafe places.
Hours after slamming the city, Trump's campaign announced on Wednesday that he will have a rally in El Paso, the home of potential Democraic challenger Beto O'Rourke, on February 11.
Nielsen called the caravan "lawless" and said it highlights the need for "comprehensive border security".
Trump had previously said he doesn't expect the talks to produce much and he's threatened to declare a national emergency to bypass Congress and build a U.S. -Mexico border wall. But the people of Texas know that the president is lying, that these are wonderful places, that they're safe cities.
The White House offered no immediate response to criticism of the president's comments about El Paso.
Trump's demand for wall funding was at the center of the recent 35-day partial government shutdown.
We mention Baltimore's crime in relation to Mr. Trump's claims about El Paso not because there's some perverse competition for which city is more unsafe but because it is the misplaced focus of the president that is itself risky.
Speaking to reporters, Tester said it was "entirely possible we could have a deal in a timely manner, which could be tomorrow but certainly by the weekend".
Trump plans to visit El Paso for a rally next week, a visit during which Margo hopes he gets a chance to show Trump the truth about his city. Still, El Paso's crime rate was and is among the lowest for USA cities of its size. Construction of a border barrier did not start until 2008 and from 2006 to 2011, the number of recorded violent crimes in El Paso increased by 17 percent.
Let's face it, this week's State of the Union address was so chalk full of lies, exaggerations and misrepresentations that bestowing the title of Alternative Fact of the Week is a fool's errand.
The AP noted that the caravan is the first in months to attempt passage through Texas rather than California.
Mulling their next move from the dusty Mexican town of Piedras Negras, just south of the Eagle Pass crossing on the US side, the latest group of around 1,700 caravan migrants want to avoid a potentially months-long wait for a chance to plead their case for asylum.
Trump also railed against illicit drugs moving through the border - but the majority of illegal narcotics don't move through the areas where Trump's wall would be built.