The Senate may soon vote on a controversial immigration bill that aims to implement new mandatory prison sentences on immigrants who illegally enter the country after being deported.

Senate Majority Leader Mitch McConnell warned Democrat leaders that he may present the immigration bill, known as "Kate's Law," before the Senate this week, reports Politico.

The bill, which is championed by Republican Sen. Ted Cruz, would crack down on illegal immigration by enforcing five-year mandatory minimum penalties on immigrants who repeatedly enter the U.S. illegally or have been convicted of an aggravated felony.

The legislation is named in honor of Kate Steinle, a 32-year-old woman who was allegedly fatally shot in San Francisco in July by a Mexican immigrant who had previously been deported five times.

The ACLU has voiced opposition to the bill, estimating that the sentencing requirements would cost $3.7 billion over the next decade. It would also require additional funding to construct 12 federal prisons that would be needed to house the immigrants, the civil rights group said.

The ACLU also wrote a letter to senators last month arguing that this "one size fits all" approach would hurt the criminal reform effort to reduce incarceration levels.

"[It] makes no sense to create new mandatory minimums for existing federal crimes that would inevitably require prison construction or illegal overcrowding in the current prison system," the letter reads.

On the other hand, Cruz and other supporters of the legislation say the measure is necessary to punish repeat offenders of immigration law.

"It is sad that the Democratic leader chooses to stand with violent criminal illegal aliens instead of the American citizens," Cruz said last week.

Cruz has also suggested that voting against the law would lead to more American citizens being killed by undocumented immigrants.

"A vote 'no' is to say the next time, the next murderer like Kate Steinle's murderer comes in, we should not enforce the laws, we shouldn't have a mandatory five-year prison sentence, instead we should continue sanctuary cities that welcome and embrace them, until perhaps it is our family members that lose their lives," the 2016 GOP presidential candidate said, according to The Huffington Post.