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Republican lawmakers are trying for the third time to pass an immigration bill that is considered a key issue for President Trump, reports The Hill.

Called 'Kate's Law,' it is named after 32-year-old Kate Steinle who was shot and killed on July 1, 2015, in San Francisco by an undocumented immigrant who had been deported multiple times, notes the Washington Times.

RELATED: Faces of Trump's immigration crackdown

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Mexican national Adalberto Magana-Gonzalez, 44, waits to be processed after being taken into custody by a U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES. TPX IMAGES OF THE DAY.

Mexican national Adalberto Magana-Gonzalez, 44, has his fingerprints taken after being taken into custody by a U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

The badge of a U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team is seen in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

U.S. Immigration and Customs Enforcement (ICE) Assistant Field Office Director Jorge Field (R), 53, arrests Mexican national Adalberto Magana-Gonzalez, 44, in San Clemente, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

Mexican national Adalberto Magana-Gonzalez, 44, waits to be processed after being taken into custody by a U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

U.S. Immigration and Customs Enforcement (ICE) Assistant Field Office Director Jorge Field (R), 53, arrests Mexican national Adalberto Magana-Gonzalez, 44, in San Clemente, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

A U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team takes immigration fugitives into custody in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

Handcuffs lie in a box at the U.S. Immigration and Customs Enforcement (ICE) Fugitive Operations office in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

U.S. Immigration and Customs Enforcement (ICE) Assistant Field Office Director Jorge Field (L), 53, arrests an Iranian immigrant in San Clemente, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

U.S. Immigration and Customs Enforcement (ICE) Assistant Field Office Director Jorge Field (R), 53, and Field Office Director David Marin arrest an Iranian immigrant in San Clemente, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

U.S. Immigration and Customs Enforcement (ICE) Assistant Field Office Director Jorge Field, 53, arrests an Iranian immigrant in San Clemente, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

A U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team member arrests an Iranian immigrant in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

A U.S. Immigration and Customs Enforcement's (ICE) Fugitive Operations team search for an immigration fugitive in Santa Ana, California, U.S., May 11, 2017. REUTERS/Lucy Nicholson SEARCH "NICHOLSON ARREST" FOR THIS STORY. SEARCH "WIDER IMAGE" FOR ALL STORIES.

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Democrats had previously blocked the bill in 2015 and 2016; last year, Senate Minority Leader Harry Reid explained that the move had to do with the expense and burden of imposing what he called "unnecessary mandatory-minimum sentences."

The current Senate version of the bill, sponsored by Texas Senator Ted Cruz, requires "a 10-year maximum prison term for an alien who re-enters after being denied admission, excluded, deported, or removed on three or more prior occasions."

SEE ALSO: Texas lawmaker threatens to shoot colleague over immigration fight

It also establishes "a 5-year mandatory minimum prison term for an alien who re-enters after being removed following a conviction for an aggravated felony or following two or more prior convictions for illegal re-entry."

The future of the Senate bill is uncertain, at least in part, because it has been folded into broader legislation involving border security.

As Lynn Tramonte, deputy director of the liberal group America's Voice, pointed out to The Hill, "...the more radical they make their bill, the less likely it is to pass."

SEE ALSO: How Trump travel ban impacts number of US visas issued

Trump has maintained a hardline stance on illegal immigration since his campaign; he even invoked Kate Steinle's name during his speech accepting the Republican presidential nomination, notes KRON.

While her brother has spoken out against Trump's use of her name and his immigration policies, her parents are reportedly suing the federal government for a number of reasons related to her death.

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GOP hopes to pass 'Kate's Law' which punishes illegal immigrants re-entering the US - AOL