A group of undocumented students and their advocates on Monday launched a round-the-clock vigil outside the Massachusetts State House in protest of a state Senate budget amendment calling for stricter measures aimed at illegal immigrants.

Holding signs and placing candles along the State House steps, members of The Student Immigrant Movement vowed to sleep under the shadow of the building — through bad weather and the threat of arrest — until the Senate withdraws the amendment or Gov. Deval Patrick vetoes it.

Andres Del Castillo, 19, of Boston, said the students had no choice but to stage a civil disobedience protest against a measure that he said would discriminate against Latinos and other immigrant groups.

"This law is actually allowing the public to racially profile," said Del Castillo, a Suffolk University student who was born in Massachusetts. "This is going to create ... an unsafe community where I'm not going to trust my neighbor because I think he might call immigration on me."

The measure, passed in the Senate last month by a 28-10 vote, would require companies doing business with the state to verify their workers are in the country legally. It also would create a toll-free phone number to report suspected illegal immigrant workers and bar children of illegal immigrants from obtaining the same in-state tuition rates to public colleges as legal Massachusetts residents.

Supporters say the measure would help curtail illegal immigration to Massachusetts and save taxpayer money, although no senator could show how it would cut costs. Still, Democratic Sen. Steve Baddour, who backed the measure after pressure from Senate Republicans, called the passage a bipartisan compromise.

The measure still must survive budget negotiations between the Senate and the House. The House narrowly rejected a similar amendment.

Patrick has not said whether he'd line-item veto the measure if it came to his desk.

"If he signs this, he might as well put himself out there as the next Brewer," said Del Castillo, referring to Arizona Gov. Jan Brewer who recently signed a controversial immigration law that has drawn nationwide protest.

Bianca Kreiling, 20, also a Suffolk University student, said the student protesters have sleeping bags and supplies needed for days. She said other advocacy groups have promised donations of supplies and money.

Six students were scheduled to spend Tuesday night on the State House steps and more are planning to camp out in the coming nights, student said.

"We'll be here for as long as it takes," said Kreiling.