NEW ORLEANS -- The driver of the party bus that crashed early Sunday in St. John the Baptist Parish blamed faulty brakes for the fatal collision, according to three people who have spoken to surviving witnesses.

Meanwhile, several elected officials in Louisiana and beyond demanded answers Tuesday regarding the immigration status of the bus driver, Denis Yasmir Amaya Rodriguez, an undocumented Honduran national who has been cited a half-dozen times for driving without a license and was arrested in 2011 on domestic abuse battery charges that were later dropped.

State Police have not yet pinpointed the cause of the multi-vehicle crash, which claimed the lives of two people, including a St. John the Baptist Parish district fire chief, and wounded more than 30 others. Authorities confirmed, however, that they are investigating whether mechanical problems caused the bus to careen into a fire engine that had been blocking traffic at the scene of an earlier wreck on Interstate 10.

"Anything's a possibility when it comes to the crash investigation," said Trooper Melissa Matey, a State Police spokeswoman. "We know speed is a factor. As to whether the brakes failed or did not fail, that's still under investigation."

Cristian Silva, a Harvey attorney who represents three of the laborers wounded aboard the bus, said that one of his clients, a woman who remained at the scene for more than an hour, heard Amaya blame the crash on malfunctioning brakes.

"The driver came out (of the bus) and said the brakes did not function," Silva said. "In her opinion, he had the opportunity to flee, and he didn't," instead remaining at the scene and helping the wounded.

Two other sources, who spoke on the condition of anonymity, said passengers on the bus had given them similar accounts of the brakes failing. One said that Amaya began swerving in an attempt to avoid striking two other vehicles before barreling into the fire engine.

Amaya remained jailed Tuesday on counts of negligent homicide, negligent injuring, reckless operation and driving without a license. Federal authorities already have issued an immigration detainer, a strong indication that he will face deportation proceedings in addition to the criminal charges.

As authorities continued to reconstruct Sunday's crash, Amaya's undocumented status – and his repeated encounters with law enforcement, dating to 2011 – fueled demands among conservatives for more stringent immigration enforcement. Louisiana Attorney General Jeff Landry on Tuesday renewed his call for the end of so-called "sanctuary city" policies in the New Orleans area, which he said "encourage the further migration of illegals into communities and cost a grave toll in money and safety."

But while New Orleans police explicitly prohibit officers from investigating immigration status in most cases, the Jefferson Parish Sheriff's Office leaves the question up to deputies' discretion, a spokesman said. And it's in Jefferson Parish where Amaya, who lived in Metairie, appears to have run afoul of the law.

Amaya, 37, has pleaded guilty at least four times, in Jefferson Parish alone, to driving without a license and avoided jail time – let alone deportation – by paying nominal fines and court costs. He also had been booked on allegations that he punched his live-in girlfriend and struck that woman's daughter with a cellphone – charges that later were dismissed.

Federal immigration officials focus primarily on deporting undocumented immigrants accused of violent crimes and other felonies. The State Police’s Matey said troopers are not trained to determine if people are in the country illegally and it depends on the circumstances of the crime whether they call federal immigration officials.

"The question is, why isn’t being in this country illegally a deportable offense?" Attorney General Jeff Landry asked. “There's no communication between the state and the feds. I was on the phone with the federal government the very next day, talking to Immigration and Customs, trying to find out why this particular person was not deported.”

Amaya's undocumented status also has drawn the ire of three Republican U.S. senators, who wrote a letter Tuesday to Jeh Johnson, the Homeland Security secretary, posing a host of questions about the pending criminal investigation and demanding a long list of documents outlining any earlier encounters immigration officials had with Amaya. In the letter, U.S. Sens. David Vitter and Bill Cassidy, R-La., and U.S. Sen. Chuck Grassley, R-Iowa, the chairman of the Senate Judiciary Committee, also asked whether U.S. Immigration and Customs Enforcement is working to determine the immigration status of the two dozen laborers aboard the party bus Amaya was driving.

"Sadly this is yet another story in a long line of stories where innocent American citizens have been killed by an illegal alien who has complete disregard for the laws of this nation," the senators wrote.

Vitter, in a separate statement, said the crash "absolutely could have been prevented, and it's important for Secretary Johnson to cooperate in investigating the illegal alien who took two innocent American lives on Sunday, including any prior criminal activity."

The Department of Homeland Security did not immediately return a call seeking comment late Tuesday. Several sources with knowledge of the investigation, however, said immigration officials have been in contact with at least some of the wounded laborers.

The Federal Motor Carrier Safety Administration, meanwhile, has assumed the lead in the investigation into Kristina's Transportation LLC, the company that provided the party bus. Duane DeBruyne, a spokesman for that agency, said investigators were working to determine whether Kristina's Transportation had been shuttling passengers across state lines and, if so, whether they had complied with federal regulations.

New details also emerged about the laborers aboard the bus and the flood-relief work they intended to perform Sunday in the aftermath of the Baton Rouge floods – work involving a contractor known as Wallace, Rush, Schmidt Inc. According to a man who said he has worked for WRS, company recruiters posted a message on social media soliciting people interested in disaster clean-up jobs.

The jobs had no benefits but paid $11 an hour, said the worker, who spoke on the condition of anonymity because he was not authorized by the company to speak with the media.

Beginning about a week before the crash, dozens of workers had been shuttled from the New Orleans area to Baton Rouge in buses owned by Kristina's Transportation, which has the trade name "AM Party Bus." Amaya had driven buses along that route on at least five occasions before Sunday, the worker said, adding that Kristina's charged about $300 per trip.

The owner of Kristina's Transportation, Christian Lombardo, had insisted that Amaya was properly licensed and even referred to the driver as "my guy Denis," the worker added. Another source, however,said Amaya had worked for years on construction sites for one of WRS' partners and a company recruiter. WRS’s attorney Jesse Wimberly said the company has no record of ever employing Amaya.

In a text message to WWL-TV, Kristina’s Transportation said, “No comment can be made at this time.”

Once the bus dropped a load of prospective workers in Baton Rouge, they would fill out applications and turn them in to WRS representatives, who would verify that the laborers had a required Social Security number and photo identification. If they had the proper documents, they would be hired; if they lacked them, they would be sent back to the New Orleans area, the WRS worker said.

On the morning of the crash, enough workers to fill three Kristina's buses were picked up outside of the Clearview Mall in Metairie, the WRS worker said. State authorities said Kristina's Transportation had the proper Public Service Commission permits to transport passengers across Louisiana parishes, but the company did not have separate papers necessary to pick them up in Jefferson Parish, parish officials have said.

Though the party bus being driven by Amaya never made it to Baton Rouge, two yellow school buses that picked up prospective laborers at the mall on Sunday did, the worker said.

The worker said he was angry with Kristina's Transportation not only because the crash left two people dead, but because it thrust laborers interested in doing vital rebuilding work into the center of a heated immigration debate that has raged throughout the presidential election cycle.

"These poor people were looking for bread to bring to the table," the worker said. "They just wanted to rebuild homes and feel that they were doing something for their community."