Updated at 3:30 p.m. with Senate vote, and 4:25 p.m. with additional comment.

WASHINGTON — Sen. Ted Cruz's legislation to impose mandatory minimum prison sentences on people who re-enter the U.S. illegally stalled in the Senate on Wednesday, the latest blow to the measure that he says would help deter illegal immigration but others warn would lead to overcrowded federal prisons.

By a 55-42 vote, Cruz's "Kate's Law" failed to advance in the Senate Wednesday. The legislation is named for Kate Steinle, a 32-year-old woman shot in San Francisco by a felon who, despite being the subject of a pending deportation order, had been released by local officials. Her death last July set off a fresh wave of debate over immigration policies and the merits of "sanctuary cities" — local governments that don’t require law enforcement to work with immigration authorities.

Cruz's proposal needed 60 votes to move forward. Due to lack of support, Kate's Law is unlikely to return before the election.

Juan Francisco Lopez-Sanchez, the man charged in the shooting, had already been deported from the U.S. five times when he was released by the San Francisco Sheriff's Department after a drug charge was dismissed. Lopez-Sanchez has acknowledged firing the gun but contends that he did not intend to shoot Steinle.

Cruz's measure, the Establishing Mandatory Minimums for Illegal Re-entry Act of 2015, has foundered in the Senate. Democrats, who along with some Republicans have voiced concern over mandatory minimums, blocked an effort to advance the bill last fall. All Republicans and three Democrats, however, supported moving the bill forward during a procedural vote on Wednesday.

Sen. Ted Cruz's bill would create a five-year minimum prison term for someone who re-enters the U.S. illegally. (Associated Press)

"The time for politics is over ... It is time to confront the sobering issue of illegal aliens, many of whom have serious criminal backgrounds, but are allowed to re-enter this country with impunity," Cruz said before the vote Wednesday.

Cruz's bill would raise the maximum criminal penalty for re-entering the country illegally from two years to five; create a new penalty of up to a decade for someone who returns illegally after three or more deportations; and create a five-year mandatory minimum for someone who has an aggravated felony before deportation or who has been convicted twice of illegal re-entry.

The former Republican presidential candidate believes his measure could have helped prevent Steinle's death and laid blame on President Barack Obama's immigration policies, though federal authorities had issued a sixth deportation order for Lopez-Sanchez.

"Clearly we are failing to adequately deter deported illegal aliens...especially those with violent criminal records," Cruz said. "We must increase the risks the penalties for those who would contemplate illegally returning to the U.S. to commit acts of murder."

The White House issued a veto threat on Wednesday, defending its immigration enforcement policies and criticizing House inaction on "the nation's broken immigration system." Kate's Law, the statement continued, "fails to offer the comprehensive reforms needed to fix the nation's broken immigration laws and would impose severe and unprecedented mandatory minimum sentences that would undermine the discretion of federal judges to make sure the punishment fits the crime in each case."

Jim Steinle, second from left, testifies next to Montgomery County (Md.) Police Chief J. Thomas Manger before a Senate Judiciary hearing. Steinle's daughter, Kate (pictured at right), was killed by a man previously deported five times.

Families Against Mandatory Minimums, a nonprofit group sentencing reform advocacy group, also came out against Kate's Law because of concerns it's too broad.

"Like all mandatory minimum sentences, passing Kate's Law might feel good, but it won't make us safer," said Molly Gill, FAMM's director of federal legislative affairs, in a statement this week. "Requiring courts to send all immigration violators to federal prison for at least five years might lock up some violent people longer, but it will definitely lock up many, many nonviolent ones longer. This mandate will cost billions of dollars, dollars better spent on fighting terrorism or supporting law enforcement and victims."

But Jon Feere, a legal policy analyst for the Center for Immigration Studies, which advocates more restrictive immigration policies, sees value in the proposal.

"If we’re serious about our sovereignty and the rule of law, there needs to be some form of punishment," he said. "If the goal is to discourage people from risking their lives, crossing the border or paying smugglers to bring them across, then this is the direction we should be moving in."

According to an analysis by the Center for American Progress, the measure would cost $3.1 billion over the next decade just to house the people with prior aggravated felony convictions, said Tom Jawetz, the center's vice president of immigration policy. That figure doesn't include people in the other categories of illegal re-entry convictions, nor the cost to build the nine additional federal prisons his center estimates will be needed.

Jawetz questioned the effectiveness of Cruz's measure, noting that the man charged with Steinle's murder had spent nearly two decades in federal prison.

"It's an extremely expensive" law, he said. "The other question is: What do you get for that cost? The truth is, there's no evidence it would deter future unauthorized migration."

Cruz dismissed the financial concerns on Wednesday, noting: "The cost of violent crime at the hands of recidivist, criminal illegal aliens is far greater than the commonsense investment to prevent crimes of violence like the horrific murder of Kate Steinle."

Cruz's bill was one of two related to Steinle's death that stalled Wednesday. Legislation that would have withheld federal funding from sanctuary cities, sponsored by Sen. Pat Toomey, R-Pa. and cosponsored by Cruz, also failed to advance.

Sen. John Cornyn, the Senate's No. 2 Republican, decried the failed votes on Wednesday, saying "votes like this" cause "people to wonder if the federal government can be trusted" with basic issues of governance.