“I will offer a substitute that is much more likely to be considered by the other body [the House] and sent on to the president for his signature,” Grassley said.

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Democrats, including President Obama, said they preferred the Democratic Senate bill because it would give tribal authorities jurisdiction over non-Indians in some domestic violence cases on tribal land, but Republicans say that issue has raised questions about possible Constitutional rights violations of U.S. citizens.

“That provision raises serious constitutional questions,” Grassley said.

Grassley expressed concern that U.S. citizens living or working on tribal land would be subject to tribal courts if accused of domestic violence or rape and would have no way to appeal the tribal court decisions in the federal court system.

“I cannot in good conscience vote for a bill that violates the Constitution,” Sen. John CornynJohn CornynSenate moving ahead with border bill, despite Trump GOP senators introduce bill to prevent family separations at border Senate GOP tries to defuse Trump border crisis MORE said Thursday. “I will however vote for the alternative from Sen. Grassley.”

Sen. Maria CantwellMaria Elaine CantwellEnergy commission sees no national security risk from coal plant closures OPEC and Russia may raise oil output under pressure from Trump Hillicon Valley: Lawmakers target Chinese tech giants | Dems move to save top cyber post | Trump gets a new CIA chief | Ryan delays election security briefing | Twitter CEO meets lawmakers MORE (D-Wash.) said Grassely's alternative is not needed because all Native American tribes have adopted the Indian Civil Rights Act, which provides all those under tribal jurisdiction the same rights provided by the Constitution.

The Senate bill also prohibits discrimination against lesbian, gay, bisexual and transgender (LGBT) citizens in grant programs to help victims, and would let some illegal immigrants stay in the country to receive help if they are victims of domestic violence or rape.

Democrats have argued that lawmakers should not pick and chose who gets protections under the law.

“Tribal provisions in this bill need to become law, yet some of my colleagues on the other side are trying to strip that out,” Sen. Mark BegichMark Peter BegichFormer Alaska senator jumps into governor race Overnight Energy: Trump directs Perry to stop coal plant closures | EPA spent ,560 on customized pens | EPA viewed postcard to Pruitt as a threat Perez creates advisory team for DNC transition MORE (D-Alaska) said. “Some members want to debate the rights of their abusers.”

Sen. Amy KlobucharAmy Jean KlobucharDem senators introduce bill to ban controversial voter purges Democrats protest Trump's immigration policy from Senate floor The Hill's Morning Report — Sponsored by PhRMA — GOP lawmakers race to find an immigration fix MORE (D-Minn.) said Grassley’s substitute would do more than just change the language on tribal jurisdiction. She said his bill would also add unnecessary provisions to reduce fraud when visas are granted to immigrant women who are abused. Klobuchar said law enforcement officers already have to certify if the immigrant is eligible for the visa. 

Democrats removed language that increased the number of visas for abused immigrants in order to make House passage more likely.

Both the House and Senate passed their own versions during the 112th Congress, but neither chamber took up the other's version. The House version didn't include provisions extending protections for victims of domestic violence to Native Americans, LGBT victims and immigrants.

VAWA provides grants to victims of domestic violence in order to encourage victims to leave their abusive situations. Some feel they can’t get away from their abusers because they might not have another form of income, so the grants can provide housing assistance and cellphones for victims. Under this reauthorization bill, these programs would continue for another five years.

Grassley said that his bill would ensure that more money goes to "victims and not bureaucrats" by requiring strict oversight into how the money is spent.

This article was updated at 3:12 p.m.