It is unclear whether any Democrats will sign onto the Succeed Act, or whether common ground can be reached between the Republican bill and the Dream Act, which has languished in Congress since 2001. To be eligible for protection under the Succeed Act, immigrants must have arrived before the age of 16 and been in the United States since June 15, 2012.

The Succeed Act also makes immigrants apply for conditional status for the first 10 years, similar to the work permits offered under DACA, after which they are allowed access to a green card. However, unlike other green card holders, those eligible under the Succeed Act would not be allowed to use their green cards to help other family members become legal residents. After five years as a green card holder, a person would be able to apply to become an American citizen.

The Dream Act is considerably more lenient.

“I appreciate that my colleagues recognize the need to pass legislation giving a path to citizenship to Dreamers, young immigrants who were brought here as children and grew up in this country — so do 75 percent of the American people,” said Senator Richard J. Durbin, Democrat of Illinois who authored the Dream Act with Mr. Hatch. “Unfortunately,” he said, the Republican bill “falls short.”

Mr. Lankford said he had talked to Mr. Trump about the bill and that the president indicated he would support it. Mr. Lankford also pushed back on conservatives who argue that legalizing so-called Dreamers would take jobs from other Americans.