Three GOP senators have introduced the anti-American Succeed Act, their own version of the anti-American DREAM Act. See that link for the huge downsides of any sort of DREAM Act, no matter what it's called and who it's from.

The GOP's version of the anti-American DREAM Act would give amnesty to hundreds of thousands of illegal aliens and, of course, Donald Trump has indicated that he's "very supportive" of the anti-American bill.

The three senators are Thom Tillis (North Carolina), James Lankford (Oklahoma), and Orrin Hatch (Utah). From [1]:

...The new Dreamer blueprint is already hitting resistance from liberal immigration advocates and conservative hard-liners, though Lankford said President Donald Trump indicated during a phone conversation with him that he was “very supportive” of the concept behind the bill.

...Tillis and Lankford have tried to address that demand by barring Dreamers who would obtain green cards through their legislation from petitioning family members, although they would be able to sponsor them if they become citizens, according to a person familiar with the legislation...

...To be eligible under the Succeed Act, an immigrant must have been in the U.S. since June 15, 2012 — the start of the Deferred Action for Childhood Arrivals program, the Obama-era executive action that Trump said he would end — and before the age of 16. They would be required to obtain a high school diploma, pass a “thorough” criminal background check, submit biometric data to the Department of Homeland Security and pay off any back taxes or establish a repayment plan.

This would give the Dreamers a “conditional permanent residence” status. If they maintained that status for 10 years, they could apply for a formal green card. Under conditional permanent residence, the Dreamers would have to earn a college degree, serve in the military for at least three years or be consistently employed.

The status would have to be renewed after five years. Once they obtain green cards, the immigrants would be required to wait for five years before they could apply for U.S. citizenship, according to the legislation. Undocumented parents of Dreamers who would qualify under the new Republican bill would be barred from petitioning to stay in the United States based on their children’s legal status....

...Tillis, a first-term senator who has expressed interest in immigration for some time, and Lankford have communicated with senior White House officials for several weeks on their bill and received a positive reception, according to one Republican source familiar with their efforts...

From [2]:

Matthew La Corte, an immigration policy analyst at the libertarian Niskanen Center, says the Succeed Act will be more palatable to conservative lawmakers than the Dream Act, a bipartisan amnesty bill favored by Democratic leadership.

“There needed to be a fresh new examination of what a Dream Act should look like, specifically from a conservative angle. This is a new, unique attempt,” said La Corte, who worked with Tillis on the legislation...

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[1] politico · com/story/2017/09/25/dreamers-republican-new-bill-243100 by Seung Min Kim
[2] d a i l y call e r · com/2017/09/25/gop-senators-aim-to-win-over-conservatives-with-tougher-dreamer-amnesty-bill by Will Racke