Sen. Ted Cruz Rafael (Ted) Edward CruzTrump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy MORE (R-Texas) will try to pass legislation on Thursday that would increase penalties for undocumented immigrants who reenter the country after being deported.

Under the legislation, undocumented immigrants could face additional prison time if they reenter the country, including a minimum five-year sentence if they were previously convicted of an aggravated felony or of illegally reentering the country twice.

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The proposal — referred to as Kate's Law after Kathryn Steinle, who was shot and killed in San Francisco by an allegedly illegal immigrant who had already been deported five times — was fast-tracked on the Senate floor Thursday. The procedural move allows it to skip the committee process and be placed directly on the Senate calendar, which could allow it to be scheduled for a vote.

The Texas Republican, who is running for president in 2016, is planning to come to the Senate floor on Thursday to ask for unanimous consent to pass the bill, according to a release from his office.

Cruz said at the time that Republican leadership should attach the proposal to must-pass legislation.

"Leadership loves to speak of what they call governing, and in Washington governing is always said at least an octave lower, governing. Well, when it comes to stopping sanctuary cities and protecting our safety, we need some governing," he said on Tuesday.

For Cruz to be successful on Thursday he'll need every senator to agree to allow for the legislation to be taken up and passed. He added in a statement that he hopes "my colleagues in the Senate will support this bill and stand with the American people — the people we should be protecting — rather than convicted felons like the murderer of Kate Steinle.”