Other states have adopted far more significant changes to voting rules. In Oregon, Washington and Colorado, all registered voters are automatically sent a mail-in-ballot, while Maine and Vermont allow felons still in jail to vote.

In New Jersey, Mr. Murphy overcame a contentious relationship with two legislative leaders — Stephen M. Sweeney, the Senate president, and Craig Coughlin, the Assembly speaker — to pass last year’s voting bills. One law, which automatically renewed mail ballots for people who had voted by mail in the 2016 election, resulted in more than 400,000 votes being cast by mail during the 2018 midterms, by far the most for any election, including presidential elections, in state history.

The changes in voting laws followed efforts that date to 2015 when Democratic lawmakers passed an act that contained versions of the proposals Mr. Murphy is now promoting, as well as new proposals like language accessibility, which would require ballots to be printed in more languages if populations were represented in significant numbers in election districts. Mr. Murphy’s predecessor, Gov. Chris Christie, a Republican, vetoed the bill, which has been reintroduced in the Assembly.

More recently, Democratic lawmakers have found themselves the target of intense criticism from voting rights activists over a controversial effort to change the way New Jersey draws its legislative districts. The proposal called for enshrining a formula into the state Constitution that would have tipped the playing field to favor Democrats.

Mr. Sweeney was a sponsor of the bill. Mr. Murphy, progressive Democratic groups and Republicans all opposed the effort; Mr. Sweeney eventually announced that he would not bring the measure for a final Senate vote.

Mr. Sweeney declined to say whether he would support Mr. Murphy’s electoral package, while Mr. Coughlin said he believed in expansive voting reforms.

“Speaker Coughlin is committed to changing New Jersey’s antiquated voting laws and will work to protect voting rights for New Jerseyans across the state,” said Liza Acevedo, a spokeswoman for Mr. Coughlin.