By Tim Reid and Nathan Layne

PHOENIX, Ariz. (Reuters) - Control of Congress was up for grabs early on Wednesday after the midterm elections yesterday, with many of the most competitive races uncalled, leaving it unclear whether Republicans would crack Democrats' tenuous hold on power.

In a critical win for President Joe Biden's party, Democrat John Fetterman flipped a Republican-held Senate seat in Pennsylvania, beating Republican celebrity doctor Mehmet Oz and bolstering his party's chances of holding the chamber.

The mood at the White House improved as the night wore on, with once-nervous aides allowing smiles to creep onto their faces and saying early signs for Democrats were better than expected. On Twitter, Biden posted a photo of himself happily congratulating some of the Democratic winners by phone.

In the House of Representatives, Republicans remained favored to win a majority that would allow them to halt Biden's legislative agenda. By early Wednesday, the party had flipped six Democratic House seats, Edison Research projected, one more than the minimum they need to take over the chamber.

That number could change. Only 13 of the 53 most competitive races, based on a Reuters analysis of the leading nonpartisan forecasters, had been decided, raising the prospect that the final outcome may not be known for some time.

The party that occupies the White House almost always loses seats in elections midway through a president's first four-year term, and Biden has struggled with low public approval for more than a year.

But Republican hopes for a "red wave" of victories faded as Democrats showed surprising resilience in several key races. Democrats were projected as the winners in 11 of the 13 close contests that had been decided.

"Definitely not a Republican wave, that's for darn sure," Senator Lindsey Graham (R-SC) told NBC in an interview.

The Democratic speaker of the House, Nancy Pelosi, said in a statement, "It is clear that House Democratic members and candidates are strongly outperforming expectations around the country."

Voter anger over the Supreme Court's June decision to overturn the nationwide right to abortion helped Democrats to curb their losses.

A Republican majority in the House, even a narrow one, would be able to block Biden's priorities while launching politically damaging investigations into his administration and family.

Senate Still In Play

The Senate was still a toss-up, with pivotal battles in Arizona, Georgia, and Nevada still in play.

The Georgia Senate race could end up in a December 6 runoff, possibly with Senate control at stake. Democrats currently control the 50-50 Senate with Vice President Kamala Harris able to break any ties.

Thirty-five Senate seats, all 435 House seats, and three dozen governors' races were on the ballot. Florida Gov. Ron DeSantis, a leading contender for the Republican presidential nomination in 2024, added to his growing national profile with a dominant victory over Democratic Rep. Charlie Crist, Edison projected.

More than 46 million Americans voted ahead of Election Day, either by mail or in person, according to data from the U.S. Election Project, and state election officials caution that counting those ballots will take time.

High inflation and abortion rights were voters' top concerns, with about three in ten voters picking one or the other as their top concern, exit polls showed. Crime, a major focus in Republican messaging in the campaign's final weeks, was the top issue for just about one in ten voters.

Competitive Districts Split

Both parties notched victories in competitive districts.

In Virginia's 2nd congressional district, Democratic U.S. Representative Elaine Luria lost to Republican challenger Jennifer Kiggans in a district Biden carried by two points. But in the state's 7th district, which Biden won in 2020 by 7 percentage points, Representative Abigail Spanberger held off a Republican challenger.

Local officials reported isolated problems across the country, including a paper shortage in a Pennsylvania county. In Maricopa County, Arizona - a key battleground - a judge rejected a Republican request to extend voting hours after some tabulation machines malfunctioned.

The problems stoked evidence-free claims among Republican former President Donald Trump and his supporters that the failures were deliberate.

Scores of Republican candidates have echoed Trump's false claims that his 2020 loss to Biden was due to widespread fraud, raising fears among Democrats that they could interfere with the 2024 presidential race.

In Pennsylvania, Republican gubernatorial candidate Doug Mastriano, who sought to overturn the state's election results after Trump lost, was defeated by Democrat Josh Shapiro. Democratic governors also fended off strong Republican challenges in Michigan and Wisconsin, two states likely to remain political battlegrounds in the 2024 presidential race.

Trump, who cast his ballot in Florida, has frequently hinted at a third presidential run. He said on Monday that he would make a "big announcement" on November 15.

Abortion Rights Secured

Voters in Michigan, Vermont, and California approved referendums enshrining abortion rights in their state constitutions; a measure that would establish Kentucky's state constitution does not protect abortion was too close to call.

The primary issue weighing on Democrats was stubbornly high annual inflation, which at 8.2 percent stands at the highest rate in 40 years.

"The economy is terrible. I blame the current administration for that," said Bethany Hadelman, who said she voted for Republican candidates in Alpharetta, Georgia.

A Reuters/Ipsos poll this week found just 39 percent of Americans approved of the way Biden has done his job. Some Democratic candidates deliberately distanced themselves from the White House as Biden's popularity languished.

Trump's polling is similarly low, with just 41 percent of respondents to a separate recent Reuters/Ipsos poll saying they viewed him favorably.

In Congress, a Republican-controlled House would be able to thwart Democratic priorities such as abortion rights and climate change, while a Republican Senate would hold sway over Biden's judicial nominations, including any Supreme Court vacancy.

Republicans could also initiate a showdown over the country's debt ceiling, which could shake financial markets.

Republicans will have the power to block aid to Ukraine if they win back control of Congress, but analysts say they are more likely to slow or pare back the flow of defense and economic assistance.

(Reporting by Joseph Ax, Jason Lange, Doina Chiacu, Susan Heavey, Moira Warburton, Gram Slattery and Trevor Hunnicutt in Washington, Gabriella Borter in Birmingham, Michigan, Nathan Layne in Alpharetta, Georgia, Masha Tsvetkova in New York, Tim Reid in Phoenix and Ned Parker in Reno, Nevada; Writing by Joseph Ax and Andy Sullivan; Editing by Scott Malone and Howard Goller)