WASHINGTON — A judicial nominee nearing a showdown vote in the Senate Judiciary Committee could be the test for Senator Jeff Flake’s vow to block judges until the Senate is allowed to vote on legislation to protect the special counsel, Robert S. Mueller III.

Democrats have united behind a bid to derail the district court nomination of a judge who defended a racially gerrymandered House map in North Carolina and helped draft the state’s voter ID law, efforts that federal courts found were specifically designed to disenfranchise African-American voters, in one case, “with almost surgical precision.”

With Mr. Flake pledging to stay true to his word, opponents need to find one more Republican to block him, a victory that would momentarily pause the stream of conservative judges Senate Republicans are sending to the federal bench. Senator Tim Scott of South Carolina, the lone black Republican in the Senate, helped sink a judicial nominee in July over his writings in college, which railed against “race-focused groups” on campus and “race-think.”

A vote is expected this week.

Thomas A. Farr, 64, a Raleigh-based attorney with a focus on employment law, would fill the nation’s oldest federal judiciary vacancy, left open since 2005. But Democrats, led by Senator Chuck Schumer and the Congressional Black Caucus, are outraged at Mr. Farr’s nomination and are spearheading a campaign against him. A coalition of progressive groups, including the N.A.A.C.P. and Demand Justice, have joined the fray.