On Tuesday, Nevada became the latest state to pass a bill that would grant its electoral votes to whoever wins the popular vote across the country, not just in Nevada. The movement is the brainchild of John Koza, a co-founder of National Popular Vote, an organization that is working to eliminate the influence of the Electoral College.

If Nevada’s governor signs the bill, the state will become the 15th — plus the District of Columbia — to join an interstate pact of states promising to switch to the new system. Those states, including Nevada, have a total of 195 electoral votes. The pact would take effect once enough states have joined to guarantee the national winner 270 electoral votes, ensuring election.

Enforcement, however, could be very difficult without congressional approval, according to constitutional law experts. And the pact would be highly vulnerable to legal challenges, they say.

But while it may seem quixotic, momentum is building. So far in 2019, Colorado, New Mexico and Delaware have passed laws joining the pact. Maine and Oregon may take similar steps this year.

Mr. Koza said he and his colleagues have been lobbying state legislators across the country since 2006 to enact such bills. An Electoral College hobbyist since the 1960s, he watched in frustration in 2004 as the presidential election between President George W. Bush and his Democratic opponent, John Kerry, came down to a few battleground states.

It wasn’t right, and it happened again, year after year, he said: “Everybody’s vote should count. But entire campaigns run around a couple of states and that, in turn, distorts government policy.”

In a presidential election, the Constitution grants states a certain number of electors, equal to their combined representation in the House and the Senate, and the electors choose the president. In general, the candidate who wins the most popular votes in each state gets all that state’s electors, though a handful of states use different rules. The candidate who gets the majority of the electoral votes becomes president.

But, as in the 2016 election, that is not always the candidate who won the overall popular vote. In 2016, former Secretary of State Hillary Clinton received some three million more votes than President Trump, but the states she won gave her fewer electoral votes than Mr. Trump received.

In all, five presidents in American history have won office while losing the popular vote, including two of the last three: Mr. Trump and Mr. Bush.

Many Democrats believe the current system unfairly favors rural states with smaller populations, which are often strongly Republican.

Of course, not everyone likes the idea of moving away from the current Electoral College system.

In Colorado, with Democrats in control of both the legislature and the governor’s seat, a measure like Nevada’s passed and was signed into law by Gov. Jared Polis in March. But it set off an outcry among conservatives in the state. No Republicans supported it.

On the state House floor, one legislator suggested renaming the measure the “We Really, Really, Really, Really, Really Hate Donald Trump Act of 2019.”

Jerry Sonnenberg, a Republican state senator in Colorado who opposed the bill, said he believed the change would weaken the electoral power of sparsely populated rural states like Wyoming and Utah, while strengthening states like California and New York.

In his view, the Electoral College was created so that “people in rural areas did not get overrun by the masses.”

“I think it’s completely appropriate that we keep the Electoral College,” he said.

For his part, Mr. Koza said the effort goes far beyond Mr. Trump. “The visible public problem right now with the electoral system is that the candidate who came in second gets the White House,” he said. “But the real problem is that very few states get the attention of the presidential campaigns.”

He believes the movement will not reach a critical mass until the 2024 election, when Mr. Trump most likely would not be on the ballot.

Sanford Levinson, a constitutional law scholar at the University of Texas at Austin, is sharply critical of the Electoral College system, but does not believe the interstate pact would solve all of the problems inherent to America’s election design.

The Constitution gives disproportionate representation to smaller states in the Electoral College, he said, but he believes the entire system should be replaced, not just circumvented. A popular majority should decide the presidency directly, he said, through runoff elections or tiered-candidate ballots.

“I want to emphasize that I rarely engage in Founder-bashing,” he said. “I don’t think these were stupid arguments in 1787. But times change.”

Even if enough states sign on to the pact to make it effective, Mr. Levinson said he anticipates significant legal challenges if the proposal is not sanctioned by Congress as well.

“What if it turns out that the Republican candidate comes in first, but doesn’t get the majority of the vote, and California says, ‘Wait, we don’t see a reason why our electors should vote for the candidate who didn’t get a majority,’” he said. “Could the other states enforce it, or not?”

Mr. Koza intends to keep pushing ahead anyway. Most state legislatures adjourn their sessions by the end of June, so for the rest of the year, he and his colleagues, including the movement’s other co-founder, Barry Fadem, will strategize about what comes next.

Mr. Koza said his approach today is similar to the one he used while lobbying to create state lotteries in the 1970s and 1980s: Take your time and build relationships, vote by vote.

“This is sort of a seasonal business — I tell people it’s like selling fruit,” Mr. Koza said.