WASHINGTON, Nov 6 (Reuters) - Democrats struck early in the battle for the U.S. House of Representatives on Tuesday, but faced an uphill climb to capture the Senate after Republican Mike Braun knocked off incumbent Democrat Joe Donnelly in Indiana.Most of the races that will decide the balance of power in Congress and shape the future of Donald Trump's presidency were still too close to call as polls closed in more than half of the 50 U.S. states. In the House, Democrat Jennifer Wexton ousted incumbent Republican Barbara Comstock in suburban Virginia outside Washington and Democrat Donna Shalala, a former Cabinet secretary under President Bill Clinton, captured the south Florida seat of a retired Republican.That gave Democrats two of the 23 seats they need to capture the Republican-held House, slam the brakes on Trump's agenda and exercise renewed oversight of his administration.In the Senate, Republicans are favored to maintain control, and Democrats must pick up two seats to win a majority. Knocking off Donnelly in Indiana makes the math difficult for Democrats, with competitive Senate races still too close to call in Florida and Texas.Incumbent Democratic Senator Joe Manchin won a hotly contested race in conservative West Virginia, and Marsha Blackburn held a Senate seat for Republicans.Senators Bernie Sanders of Vermont, a 2016 Democratic presidential contender, and Tim Kaine of Virginia, Hillary Clinton's vice presidential nominee in 2016, easily won re-election, news networks projected. Democratic Senator Sherrod Brown was projected to hold his seat in Ohio.High-profile races for governor in Georgia, Florida and Ohio also were too close to call. A full picture of the voting results were not expected for hours, with many of the most important races considered toss-ups heading into Election Day.The first national elections since Trump captured the White House in a 2016 upset became a referendum on the polarizing president, and a test of whether Democrats can turn the energy of the liberal anti-Trump resistance into victories at the ballot box.The Democrats were favored by election forecasters to pick up the 23 seats in the House, but opinion polls showed they had slimmer hopes in the Senate. All 435 seats in the House, 35 seats in the 100-member Senate and 36 of the 50 state governorships were up for grabs.The volatile midterm campaign was marked by clashes over race, immigration and trade. In the final stretch, Trump hardened his rhetoric on issues that appealed to his conservative core supporters, issuing warnings about a caravan of Latin American migrants headed to the border with Mexico and condemnations of what he called U.S. liberal "mobs."Many Democrats, already benefiting from anti-Trump enthusiasm, focused on bread-and-butter issues like maintaining health insurance protections for people with pre-existing medical conditions and safeguarding the Social Security retirement and Medicare healthcare programs for the elderly.If Democrats capture the House, they could launch congressional investigations into Trump's administration, including his tax returns, possible business conflicts of interest and the nature of his 2016 campaign's ties to Russia.A Republican victory in both chambers of Congress would be a validation for Trump's polarizing style, a month after he solidified a conservative majority on the Supreme Court when the Senate confirmed his nominee Brett Kavanaugh after a fight over sexual misconduct accusations against the jurist.Striking a dark tone at a rally in Indiana on Monday evening, Trump accused Democrats without offering any evidence of "openly encouraging millions of illegal aliens to break our laws, violate our borders and overrun our country."Ahead of the results, U.S. stocks closed higher, with the benchmark S&P 500 Index ending the day at a two-week high. U.S. Treasury securities prices fell, and the 10-year yield closed at its highest level since 2011. The dollar was unchanged.SOME VOTING PROBLEMS REPORTEDProblems with voting machines prevented Americans from casting ballots in a dozen states, U.S. rights advocates said, following complaints about registration problems, faulty equipment and intimidation received during early balloting.A U.S. Department of Homeland Security official said the reports of voting technology failures appeared so far to have had no significant impact in preventing people from voting.Voter turnout, normally lower when the presidency is not at stake, could be the highest for a midterm election in 50 years, experts predicted. About 40 million early votes were likely cast, said Michael McDonald, a professor at the University of Florida who tracks the figures. In the last such congressional elections in 2014, there were 27.5 million early votes."I have worked at this poll the last three elections and this is the biggest turnout ever," said Bev Heidgerken, 67, a volunteer at a polling place in Davenport, Iowa.At least 64 House races remain competitive, according to a Reuters analysis of the three top non-partisan forecasters, and Senate control was expected to come down to a half dozen close contests in Arizona, Nevada, Missouri, North Dakota, Indiana and Florida.In his time in office, Trump has pushed tax cuts through Congress and overseen a period of economic and jobs growth but has failed so far to deliver on presidential campaign promises to replace the Obamacare healthcare law and build a wall on the Mexican border that he has said is needed to battle illegal immigration.DEMOCRATIC PUSHBACKA Democratic victory in the House would further hinder the border wall plan and complicate congressional approval of a deal to update the North American Free Trade Agreement.Trump also could face more pushback from Democrats on trade tariffs he has introduced, especially in farm states hard hit by retaliatory measures from China or manufacturing states hit by higher steel and aluminum prices.A debate about whether Trump's inflammatory rhetoric encouraged extremists erupted in the campaign's final weeks after pipe bombs were mailed to his top political rivals allegedly by a Trump supporter who was arrested and charged, and 11 people were killed in a shooting at a Pittsburgh synagogue.It was the first national election in the United States since the 2016 race in which Russia interfered, according to U.S. intelligence agencies, with a campaign of hacking and propaganda to sow discord, harm the Democratic presidential candidate and boost Trump's chances. Russia denies meddling.