Election Day is a month away, and the polls show a breathtakingly close race. Vice President Harris has a small lead nationwide. She led former President Trump by 3.4 points in the average maintained by The Hill/Decision Desk HQ (DDHQ) as of Friday evening. But the picture in the battleground states is tighter still. Of the seven battlegrounds likely to decide the election, Harris leads in four states and Trump in three. But neither candidate is ahead in any of those critical states by more than 2 percentage points. In five of the states, the margin for the leading candidate is less than 1 point. The campaigns will now be furiously battling it out on the campaign trail and in TV ads to try to drive turnout among their supporters and win over late-deciding voters. The Trump campaign and its affiliated committees have said they began October with $283 million cash on hand. The Harris campaign has yet to release its fundraising numbers for September.  Bloomberg, citing data from AdImpact, has reported that Team Harris spent $192 million on advertising to Trump’s $72 million during September. Here is where things stand in the battlegrounds. Arizona Trump has a tiny lead here, up by eight-tenths of a percentage point in The Hill/DDHQ average. Arizona is the only battleground state that abuts the border, making immigration — one of Trump’s strongest issues — especially salient. A CNN/SSRS poll late last month found Trump had a 16-point lead nationwide, 50 percent to 34 percent, when registered voters were asked which candidate they trusted more on immigration. An Emerson College poll released this week gave Trump a 4-point lead in the Grand Canyon State among likely voters, though another survey from HighGround put Harris up by 2 points. Arizona was one of the closest states in 2020. President Biden won by roughly one-third of a point. Georgia Trump is up by seven-tenths of a point in the state that gave Biden his narrowest win in percentage terms in 2020. Biden’s victory made him the first Democrat since President Clinton in 1992 to carry Georgia in a presidential election. Harris may be lagging by a fraction but, as in North Carolina, she has at least made Georgia truly competitive — which it may not have been if Biden had remained in the race. In Biden’s final weeks as a candidate, Trump was leading comfortably. Turnout among Black Americans will be pivotal in a state where 33 percent of the population is African American. Trump appeared Friday with Georgia Gov. Brian Kemp (R) as the two were briefed on storm damage from Hurricane Helene. The two have had a tumultuous relationship, stemming from Kemp’s refusal to go along with Trump’s attempts to overturn the 2020 election result in the state. Michigan Polls have tightened in the Wolverine State.  Harris leads by just two-tenths of a point in The Hill/DDHQ average. In late August, around the time of the Democratic National Convention, Harris led by almost 2 points. When the margins are so narrow, it’s hard to identify a particular cause of poll movement. It could be that a small convention bounce for Harris has faded, or that the polls are showing some statistical “noise” rather than any substantive movement. But the growing crisis in the Middle East is especially salient in Michigan, which has the highest concentration of Arab Americans in the nation. Around 200,000 Arab Americans live in the state, which Biden won by roughly 150,000 votes in 2020 and Democratic nominee Hillary Clinton lost by fewer than 11,000 votes in 2016. “No administration has helped Israel more than I have — none, none, none,” Biden told reporters during a surprise appearance in the White House briefing room Friday. That could be a problem for Harris in Michigan. Nevada Harris has her biggest battleground lead in Nevada. She’s up by exactly 2 points in The Hill/DDHQ average. That may be partly a consequence of Nevada’s increasing Democratic tilt in recent years. President George W. Bush carried the state twice, but no Republican has won it since. The powerful Culinary Workers Union Local 226 — which represents many of the hospitality workers in Las Vegas and Reno — endorsed Harris back in August. It’s also notable that Harris has adopted a Trump proposal — making tip income exempt from income tax — which has particular appeal to workers in the hospitality industry. North Carolina North Carolina is the only one of this year’s battlegrounds that Trump carried in 2020. Harris currently trails by just eight-tenths of a point in TheHill/DDHQ average.  History appears to be on Trump’s side. President Obama is the sole Democrat since 1976 to carry the Tar Heel State — and even then he managed the feat in only the first of his two campaigns. On the other hand, two demographic elements could help Harris. North Carolina’s population is 22 percent Black, and those voters could turn out in large number for a candidate vying to become the first female Black president. In Census Bureau figures, North Carolina also has a larger share of the population with a bachelor’s degree or higher than any other battleground. In recent years, college graduates have increasingly favored Democrats.  In 2020, Biden won college graduates by 12 points nationally over Trump, according to exit polls. Pennsylvania The Keystone State is the closest thing to a must-win this year. The most populous battleground state holds 19 electoral college votes. Harris leads by eight-tenths of a point in The Hill/DDHQ average.  On Saturday, Trump will return to Butler, Pa. — the site of the July assassination attempt against him — for a rally. Harris has also been a frequent visitor to the state — and Obama will seek to help her with a rally appearance in Pittsburgh on Oct. 10. Just how close is the state? At least five major polls since mid-September have shown the race in an exact tie. For Harris, the key is getting the biggest possible turnout among Black voters and affluent, liberal white voters, especially in the state’s biggest cities. Trump will be hoping for strong turnout in the state’s rural and exurban areas, which lean much more conservative.  The older-than-65 group make up a larger share of the population in Pennsylvania than in any other battleground. It is also one of the whitest of the battleground states. Wisconsin Harris is up by 1.3 percentage points here in The Hill/DDHQ average. Unfortunately for her, Wisconsin polls have also been among the most unreliable in the nation in recent times. The final RealClearPolitics average in the state in 2016 had Clinton up by more than 6 points only for Trump to win a narrow victory. In 2020, the Wisconsin RealClearPolitics average had Biden up by almost 7 points, and he scraped through by less than a point. Also, even though Harris leads here, her edge has come down significantly. In late August, she led by more than 4 points in the DDHQ average. Wisconsin, like many other states, is inherently hard to predict because of the possible impact of the abortion issue — a topic that is plainly to Democrats’ electoral advantage. In 2022, Roe v. Wade was struck down by the Supreme Court, a 19th century law banning almost all abortions went into effect in Wisconsin, and Democratic Gov. Tony Evers, a top GOP target, won reelection by about 3 points.