Democrats are already strongly confident of victory in three of them — Colorado, Nevada and Virginia — and believe that a fourth, North Carolina, is likely to break their way as well. Added to the party’s daunting advantage in the Electoral College, these states have impeded Mr. Trump’s path to amassing the 270 electoral votes needed to win, limiting his ability to exploit Mrs. Clinton’s late vulnerabilities and forcing him to scrounge for unlikely support in solidly Democratic places like Michigan and New Mexico.
The shift is stark enough that Democrats are pressing for victory in Arizona and Georgia, two historically Republican strongholds, while Mrs. Clinton’s standing has wobbled in familiar battlegrounds like Ohio and Iowa.
Mrs. Clinton has moved aggressively on Arizona, seeing it as a substitute for any losses in the Midwest. She plans to campaign in Phoenix on Wednesday; her running mate, Senator Tim Kaine of Virginia, will be there and in Tucson on Thursday; and she and her allies have poured millions of dollars into commercials in Arizona and Georgia, which they view as a longer-shot target.
Looking beyond the election, Republicans fear that Mr. Trump’s geographic dilemma could offer a grim glimpse of their party’s future: Unless they can win back constituencies he has driven away, the two fastest-growing regions of the country may continue to move decisively toward the Democrats.
“I think we may be seeing the ground shift under us,” said Senator Tom Udall, Democrat of New Mexico, a member of one of the West’s most enduring political families. “This may be a major political turning point.” Of Mr. Trump, he said, “He’s done some real damage nationally and in the West to Republicans by using some of the nastiest, angriest rhetoric we’ve ever had in politics.”
While Mr. Trump is running a racially tinged campaign of restoration, pledging to make America great again, minority voters in the states that increasingly decide presidential elections have been working to harness their newfound political power.
In Nevada, which has the fastest-growing populations of both Hispanics and Asian-Americans, the new immigrant blocs have become political powerhouses. Early voting data shows Democrats with such a clear lead in the state that the race may be decided there well before Election Day.
“People are organized that have never been organized before,” said Senator Harry Reid, the Democratic leader whose career in Congress began when Nevada was awarded a second House seat in 1982.
Many leading Republicans, alarmed by Mr. Trump’s candidacy and intimately familiar with the demographic shifts underway, believe the party must immediately change course after this election.
“You’ve got to stop alienating large swaths of the electorate,” said Senator Cory Gardner, Republican of Colorado, who has withdrawn his support for Mr. Trump. “And I don’t just mean in the Hispanic community — I mean Hispanics, Asians, communities of color and women.”
Mr. Trump, as the face of the Republican Party, has acted as a kind of political accelerant in the South and West, helping Democrats mobilize in the demographically diverse suburbs around cities like Atlanta and Phoenix.
Stacey Abrams, the Democratic leader in the Georgia House of Representatives, said the presidential race had been a “godsend election,” opening the eyes of national Democrats to unimagined opportunities in her state. Priorities USA Action, a “super PAC” supporting Mrs. Clinton, is spending more than $2 million in Georgia.
Shaking hands last week in a lunchtime crowd at a mall in south DeKalb County, Ms. Abrams said the electoral calculus in Georgia had changed sharply. The booming Atlanta suburbs, she said, had opened a path to victory without winning over white conservatives — but only if Democrats were able to turn out black voters and other minorities effectively.
“Trump was helpful, because it allowed people to move past the prejudice that said, you should never even think about a Deep South state being in play,” Ms. Abrams said. The dictum that elections in the South are decided by white voters, she added, “is no longer true in the Deep South.”
Democrats say Georgia is unlikely to put Mrs. Clinton over the top in the presidential race, and would tip her way only in the event of a sizable win nationally. But for Democrats to even compete there is a sign of how far into the South they have ventured.
Anthony Foxx, the federal transportation secretary and a former mayor of Charlotte, N.C., said it was almost “unavoidable” that states from Virginia to Georgia would turn blue, absent a major overhaul of the Republican Party.
“What people are seeing now is that the demographic trends in North Carolina and several other Southern states are moving in an unchangeable direction toward more progressive politics,” Mr. Foxx, a Democrat, said.
Bolstered by carefully drawn legislative maps and the results of nonpresidential elections, in which minority turnout usually dips, Republicans have maintained an iron grip on state government in places like Georgia and North Carolina, as well as some Western states.
But Republican leaders acknowledged that a moment of reckoning was ahead, perhaps sooner than expected because of this year’s presidential contest. State Representative B. J. Pak of Georgia, a Republican of Korean descent, said that he doubted that Mrs. Clinton would win the state but that his party’s leaders were acutely aware of the fast-changing terrain.
Mr. Pak, who represents Gwinnett County, a booming suburban area near Atlanta where minorities now outnumber whites, said it had been hard this year to recruit a diverse slate of candidates, or to win over women and minorities.
“Donald Trump has really made it extremely difficult,” said Mr. Pak, who has not endorsed Mr. Trump. “They feel that the party’s not welcoming, and that’s a tremendous challenge when you’re trying to get people to give the party a chance.”
Bob McDonnell, the former governor of Virginia, whose 2009 election marked the last major Republican victory in a once-reliably red state, said his party must embrace “the new Americans, the immigrants that are really kind of remaking America, like how the Irish did in the mid-1800s.” He noted that he had learned phrases in Korean and Mandarin to campaign in Northern Virginia.
“We get accused, as conservatives, of writing off certain groups of people because they don’t fit a certain political stereotype. You can’t do that as a Republican,” Mr. McDonnell said. “It’s a recipe for certain minority status.”
Senator Jeff Flake, Republican of Arizona, feels just as strongly about the need for the party to expand its reach to members of minority groups — and argues that a crucial ingredient in doing so is to pass a comprehensive immigration overhaul.
“You can’t win statewide here if you take completely unreasonable positions on immigration,” said Mr. Flake, one of the country’s most outspoken anti-Trump Republicans.
Arizona’s tumultuous internal politics have made it especially inviting for Mrs. Clinton, and most likely an easier pickup in the last week of the race than Georgia.
For the past decade, the question of what to do about the estimated 12 million immigrants in the country illegally has cleaved the Republican Party. Perhaps nowhere has it proved more divisive than in Arizona, where most schoolchildren from kindergarten to eighth grade are Hispanic.
While Mr. Flake and his Republican colleague, Senator John McCain, have led the charge for what critics call an amnesty, Sheriff Joe Arpaio of Maricopa County attained national prominence with his harsh treatment of Hispanic migrants. Mr. Arpaio’s re-election bid and Mr. Trump’s campaign have galvanized the state’s Latino residents, whose presence on the voter rolls has lagged their representation in the population over all.
Seizing on this energy, Mrs. Clinton’s campaign has redeployed staff to Arizona and has dispatched top-shelf surrogates, including Michelle Obama and Senator Bernie Sanders of Vermont, to campaign there.
Janet Napolitano, a former Democratic governor of the state, said that Mrs. Clinton could win Arizona, but that a victory was by no means “in the bag.” Yet Ms. Napolitano said that, win or lose, there was no going back.
Western Democrats cautioned that the national party should not interpret victory in 2016 as approval of a strongly ideological agenda, as much as rejection of Mr. Trump by a changing region.
“When either party wins a decisive election, they feel that it’s a validation of the most extreme parts of the party,” said Gov. John Hickenlooper of Colorado, a Democrat. “But that isn’t always what people are voting for.”
Until Republicans recalibrate their approach and project a more inclusive message, Democrats believe their future is as limitless as the Arizona desert can feel.
As he and his wife left the Casa Grande Democratic offices for their daily round of canvassing, Lee Seabolt, 70, said the Republican quandary was a matter of simple arithmetic.
“There are a whole lot more old white men like me who are going to be dying over the next four years,” he said, “and there are a lot of Hispanics who are going to be turning 18 who are going to start voting.”