WASHINGTON — The last time Republicans in the North Carolina Legislature enacted a law making it harder for some of the state’s residents to vote, a federal court said the statute targeted African-American voters “with almost surgical precision,” and threw it out.

That was last year. Now the legislators are back with a new set of election proposals, and an unconventional plan to make them stick.

Shortly before midnight on Wednesday, Republican senators unveiled legislation that would eliminate the final Saturday of early voting in state elections, a day that typically draws a large share of black voters to the polls. That followed a Republican proposal last week to place a constitutional amendment on the November ballot that would require all voters to display a photo ID before casting votes.

In addition, party leaders say they are preparing a constitutional amendment that would curb the power of the Democratic governor, Roy Cooper, over the state board that controls election procedures.