Representative Ted Deutch, a Florida Democrat, shared a video of Mr. McConnell’s remarks and said, “An Election Day holiday WOULD be a power grab,” adding: “It would be the American people grabbing power back from the wealthy special interests that dominate Washington because @senatemajldr & others prefer that it be hard to vote.”

The target of Mr. McConnell’s comments, a House of Representatives bill titled For the People Act of 2019, is the first major legislation by the new Democratic-controlled House and puts forward seven major changes to elections nationwide. The proposals are wide ranging, including changes to how people register to vote and new requirements for states to secure voting systems.

Among the proposals: Voters could register in person on the day of an election, an option that is currently offered in only 18 states and the District of Columbia, and could cast ballots in federal elections during an early-voting period, which all but 11 states already allow. Permitting same-day registration could increase voter turnout by three percentage points, the equivalent of about 3.8 million additional voters in the 2016 presidential election, according to studies. The bill would also allow automatic registration for eligible people.

The bill also seeks to remove a major hurdle that prevents people from voting: work. A census survey of roughly 19 million registered voters who did not participate in the 2016 election found that 14.3 percent, or about 2.7 million people, said they were too busy to vote. The legislation proposes making Election Day, the first Tuesday in November, a public holiday just like Washington’s Birthday, Independence Day and Christmas.

It would grant the federal government’s two million full-time employees a paid day off, and would make companies, many of which shut down on federal holidays, more likely to grant their workers a day off. Mr. McConnell derided that idea as “generous new benefits for federal bureaucrats and government employees.”