Republicans remain the favorites to win control of the House of Representatives in the midterm elections, but Democrats, who for over a year have braced for large losses, are finishing the summer in a stronger position than where they started.

Public polling and recent election results are prompting Democrats, nonpartisan election observers and some Republicans to expect a more competitive battle this fall. Republicans need just a handful of seat pickups to take over the House, which Democrats currently control 220-211 with four vacancies.

“The party in power typically doesn’t improve its electoral prospects in the final months of a midterm, but that’s where we appear to be,” Nathan Gonzales and Jacob Rubashkin of Inside Elections, a nonpartisan election watcher, wrote in a report.

The analysts cited various factors helping Democrats as they try to close the gap. Those include the fight over abortion access, weak GOP candidates in key races, investigations focused on former President Donald Trump and a recent drop in gasoline prices. They added that districts that Mr. Biden carried by at least 10 percentage points seemed more out of reach for the GOP than at this point last year.

The nonpartisan Cook Political Report lowered its projection for GOP pickups to a range of 10-20 seats, still enough to win the chamber but down from 15-30 seats previously. Cook also said it couldn’t rule out the possibility that Democrats retain their majority, citing elevated Democratic turnout.

Jaime Harrison, chair of the Democratic National Committee, predicted Sunday that the midterms will see Democrats gain seats in the U.S. Senate, pick up some governors’ mansions and hold onto their majority in the House of Representatives. “That momentum is real,” he said on CBS’s “Face the Nation” news show.

Maryland Gov. Larry Hogan, a moderate Republican, said he fears the GOP will fail to retake the Senate or pick up gubernatorial seats, though he still thinks the party will win the House.

Larry Hogan, Maryland’s Republican governor, fears the GOP will fail to retake the Senate or pick up gubernatorial seats, though he thinks the party will win the House.

Photo: Brian Witte/Associated Press

“This should be a really huge year for Republicans just because of the failures of the Democrats who are in control of everything and Biden’s low approval ratings,” Mr. Hogan said on CBS. “But we could blow it by nominating unelectable people—and that’s exactly what’s happening across the country and why the wave is going to be more of a ripple rather than a tidal wave.”

Republicans at the National Republican Congressional Committee, the House GOP’s campaign arm, say Mr. Biden’s stewardship of the economy, which shrank for a second quarter in a row amid inflation that has touched 40-year highs, will catapult the party to victory. Also, the party that controls the White House typically loses seats in the midterms.

One late development that could complicate the election outlook is a plan unveiled by President Biden this past week to cancel student debt, a move demanded by many progressives but criticized by some Democrats in competitive races. Republicans called it a handout to college graduates at the expense of other voters. The resolution of probes surrounding Mr. Trump—including a Justice Department investigation and the findings of a House panel looking into the Jan. 6, 2021, Capitol riot—could also affect the midterm result.

With their outlook brightening, some Democrats are switching gears, putting more money into ads against Republican incumbents in tight races such as Reps. David Valadao of California, Yvette Herrell of New Mexico and Steve Chabot of Ohio.

House Majority PAC, a major outside group supporting House Democrats, this past week made more than $500,000 in new fall advertising reservations in those districts, officials said. “Given the data we’re seeing out of the last few months, we are playing offense,” said Ali Lapp, the group’s president.

One Republican strategist working on House races said that Democratic enthusiasm to vote has increased following the overturning of Roe v. Wade by the Supreme Court, but Republicans still felt confident wading into districts that Mr. Biden carried due to a perceived advantage on the economy.

“We’ve seen that voters are still more concerned about inflation and the rising cost of living. That’s not to say that voters are not concerned about abortion, because it certainly registers,” this person said. The person added that Republicans candidates will need to calibrate their stance on abortion in the general election to keep in step with their districts.

Public polling has shown Republicans’ advantages moderating. For much of this year, the GOP held a slim advantage over Democrats when pollsters asked voters which party they’d prefer to see in control of Congress, according to FiveThirtyEight, which aggregates top public-opinion surveys. Democrats have regained a slim, half-percentage point advantage this month, suggesting public preference is neck-and-neck.

Mr. Biden’s approval rating has ticked up in some recent polls after hovering around 40%. A recent Gallup survey put Mr. Biden’s approval at 44%, his best number in that poll in a year.

Pat Ryan’s win in a special election for a House seat in New York’s Hudson Valley last week boosted Democrats’ hopes they can retain control of the House in November.

Photo: Mary Altaffer/Associated Press

A win by Democrat Pat Ryan to fill an open U.S. House seat in New York’s Hudson Valley gave his party a jolt of good news last week, pointing to the potential importance of abortion this fall. Mr. Ryan centered his candidacy on a fight for nationwide abortion access.

The outcome in the Hudson Valley district came after both parties were surprised earlier this month when 60% of voters in Kansas rejected a referendum that would have explicitly stated there is no right to abortion in the state’s constitution. Democrats have noted that since the Supreme Court decision, several states have seen more women registering to vote than men.

Republicans argue special elections aren’t always reflective of the broader, general election environment. November could see “a little more turnout on the Republican side,” said Sarah Chamberlain, the head of Republican Main Street Partnership, a group that backs some GOP centrists in tight races this fall. She pointed to general economic malaise as a headwind for Democrats.

Democrats also say they are going into the fall with new laws that candidates can pitch to voters. Mr. Biden recently signed a $280 billion law, which garnered some GOP support, aimed at boosting U.S. semiconductor manufacturing and competitiveness with China. He also signed a Democratic-backed healthcare, climate and tax package called the Inflation Reduction Act that Republicans opposed, saying it could derail the economy.

In town halls this month, Democratic Rep. Elissa Slotkin of Michigan has embraced the chips bill as she tries to win re-election in a district that stretches from Lansing to suburban Detroit, home to auto makers that rely on semiconductors. She also touted the Democrats’ climate, healthcare and tax law’s most immediate effects, including caps on insulin costs for Medicare beneficiaries. But she said she still hears concerns from voters about rising costs.

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“I think it’s hard to answer someone who is literally paying more for groceries than they paid a year ago that this bill is going to have a direct impact on their grocery bill. Right? I don’t B-S people about that,” she said in an interview.

Ms. Slotkin, whose district voted for Mr. Trump in 2020, said she tells voters there is no silver bullet to lower inflation, but she supports suspending federal gasoline taxes, a proposal that has faced skepticism from House leaders. Like other Democratic lawmakers in competitive districts, she criticized Mr. Biden’s package to cancel student debt, calling it “a one-time Band-Aid” that doesn’t address “the core issue of college affordability.”

Her opponent, Republican state lawmaker Tom Barrett, said he would try to use Ms. Slotkin’s vote for the Inflation Reduction Act against her, calling it an ineffective way to ease rising prices. Mr. Barrett also said Mr. Biden’s student debt cancellation plan would add to inflation and turn off independent voters.

“The overwhelming concern that [voters] are facing,” Mr. Barrett said, “are the issues of economics and security.”

Paul Kiernan contributed to this article.

Write to Joshua Jamerson at joshua.jamerson@wsj.com