Republicans won control of the Senate Tuesday evening as GOP candidates across the country swept to victory in crucial midterm elections, reflecting widespread unease about the nation’s direction and the electorate’s disenchantment with President Obama.

The GOP took control of Democratic held seats in Arkansas, Colorado, Iowa, Montana, North Carolina, South Dakota and West Virginia, giving the party seven additional senators. It had needed six to control the chamber for the first time since 2007.

The rapid-fire victories represented a repudiation of the president, who rode into office on a mantle of change in 2008 and was re-elected in 2012 but whose second term has bogged down in a problems ranging from crises abroad to the arrival of Ebola in the United States. Throughout the hard-fought the campaign, Obama was a target of Republican candidates and in the end was reduced to campaigning only in secure Democratic bastions.

“We are heading to Washington…and we are going to make ‘em squeal!” a jubilant state Sen. Joni Ernst told cheering supporters in Iowa, where she defeated Democratic Rep. Bruce Braley in the seventh GOP pickup of a Democratic-held seat.

As polls closed in Arkansas, where Rep. Tom Cotton (R) captured incumbent Sen. Mark Pryor’s Senate seat, Sen. John Boozman said the results were more a “referendum” on the president than a statement about the Republican Party and its agenda.

“Our party did better with its operation and it had better candidates, but this election was about what was occurring in the country and the world,’’ Boozman, the state’s incumbent Republican senator said in an interview. “People are concerned about the Middle East, they’re worried about what’s happening at home. That created this atmosphere for Republicans.”

The Republican-controlled Senate, which will take office in January, is expected to complicate Obama’s agenda in ways large and small. Not only will his nominees face tougher Senate scrutiny, his push for a sweeping international climate change agreement will face resistence. Republicans are expected to demand approval of the controversial Keystone XL pipeline and to push to dismantle key pieces of the Affordable Care Act.

The Senate is expected to be led by Minority Leader Mitch McConnell (R), a savvy old-guard Republican who on Tuesday easily brushed off a high-profile Democrat heavily backed by national party leaders. “I work hard to bring your concerns to D.C., and I will not let up,’’ a triumphant McConnell told cheering supporters in Louisville. He offered praise for his opponent, Alison Lundergan Grimes, saying she “ran a spirited campaign, she earned a lot of votes and she earned my respect.’

Democrats fought back by defending a seat the GOP had hoped to claim, as incumbent New Hampshire Sen. Jeanne Shaheen rebuffed a strong challenge from Republican Scott Brown. But other GOP candidates over-performed their already strong performances that the final pre-election polls had captured.

Sen. Pat Roberts (R), who had appeared on the verge of losing to indepdent Greg Orman, pulled out a narrow victory. And Virginia Democratic Sen. Mark Warner — the state’s most popular politician for a decade — was locked in an unexpectedly tight race with Republican strategist and challenger Ed Gillespie.

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The final sweep of the GOP victory was still not known Tuesday evening. Another state where the party mounted a strong Senate challenge, Louisiana, is going to a runoff election. Another closely fought Democratic held seat, Alaska, may still be counting votes for days.

In West Virginia, Republican Rep. Shelley Moore Capito defeated Natalie Tennant, overcoming support from national Democrats such as populist firebrand Sen. Elizabeth Warren (Mass.) who had campaigned for the underdog Democrat.

In Arkansas, Rep. Tom Cotton defeated incumbent Sen. Mark Pryor, while in South Dakota, former Republican governor Mike Rounds defeated a Democratic challenger along with independent former GOP senator Larry Pressler.

As expected, Rep. Steve Daines (R) easily picked off another Senate seat for the GOP after the Democratic field imploded.

Virginia Democratic Sen. Mark Warner — the state’s most popular politician for a decade — was locked in an unexpectedly tight race with Republican strategist and challenger Ed Gillespie.

McConnell and Capito, a close ally of House Speaker John Boehner (R-Ohio), are considered members of the Republican Party’s moderate wing, which could presage a good night for moderates who have been clashing periodically with their party’s conservative wing in recent years.

Although recent polls had forecast that McConnell would survive a tough challenge from Grimes, his victory was no sure thing earlier in the year.

Before the returns started coming in for Senate, House and gubernatorial races, preliminary network exit polls revealed an electorate that was largely frustrated by the political stalemate in Washington after two years in which little of legislative significance was accomplished.

Nearly 6 in 10 voters said they were “dissatisfied” or “angry” at the Obama administration, with a similar proportion feeling the same about Republican leaders in Congress.

Calling into a Connecticut radio program Tuesday, Obama urged the public to cast their votes and emphasized they “can’t afford to be cynical. Now is the precise time ordinary folks casting a ballot can break the gridlock.’’

In the West Virginia race, Capito’s victory was also significant because the state has never elected a female senator. It did elect a female House member before Capito: the late Democrat Elizabeth Kee, who was a player in helping John F. Kennedy win the 1960 Democratic presidential primary in the state.

Capito touted her family’s deep roots during the campaign -- her father, Arch A. Moore Jr., 91, is a former governor -- and her distance from the Republican Party’s conservative tea party wing.

Inside the House GOP cloakroom, Capito is generally known as an even-tempered Republican who rarely causes trouble for Boehner. She used to serve on the Rules Committee, which controls the flow of legislation on the House floor, but now sits on the Financial Services Committee and often appears on CNBC discussing financial policy

Obama has tried to convince the public of his administration’s progress, especially on the economy. The exit surveys found 40 percent of voters rated the economy as the most important issues, but despite signs of modest improvements — unemployment below 6 percent, the stock market surging and gas prices dropping — the electorate expressed a generally pessimistic view.

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One-quarter of voters said health care was the top issue in their vote, while about one in seven said foreign policy or illegal immigration was most important.

About three-quarters of voters who had turned out are white — compared with 77 percent in 2010 and 72 percent in 2012. The split between Democrats and Republicans was an even 35 percent each in 2010, but early exit polls this year showed a narrow tilt toward Democrats.

The first voting stations opened at 6 a.m. on the East Coast and the final polls are set to close in the Aleutian Islands in the Pacific 19 hours later. Even then, the final determination of who will control the upper chamber might not be known, as a potential runoff in Louisiana and the counting of votes in other states could leave the outcome in doubt for weeks longer.

Republicans were poised to make gains in both chambers of Congress amid widespread dissatisfaction with Obama’s record over the past two years, but the crucial question remained whether the GOP would pick up a net six seats to take back control of the Senate.

In all, there are 13 states where Senate seats might change from one party to the other. Republicans need to win nine of them to attain a 51-seat majority. As the polls opened, GOP candidates seemed to be leading, by a lot or by a little, in eight of those races.

McConnell (R-Ky.), who potentially stands to gain more than anyone if the Senate flips control, had earlier cast his ballot at a university in Louisville.

“I think we’re going to have a good day here in Kentucky and hopefully around the country,” McConnell told reporters as he exited Bellarmine University’s Knights Hall on the eastern side of Louisville, one of the most liberal precincts in the state.

McConnell and his wife, former labor secretary Elaine Chao, cast their votes amid a throng of local, national and international media but only a few other residents.

At the White House, after making his final campaign appearances for Democratic candidates over the weekend, Obama was projecting an air of business as usual. His daily schedule showed private meetings with International Monetary Fund Managing Director Christine Lagarde, Defense Secretary Chuck Hagel and his national security and public health teams to discuss the Ebola response.

Press secretary Josh Earnest had said Obama had done all he could to help raise money and support fellow Democrats, and the spokesman expressed confidence that “Democrats will retain the majority” in the Senate. Obama has been focusing his direct campaign efforts on Democratic governors in bluer states and staying out of races for Senate candidates in more conservative states who fear his involvement could be a liability.

On Tuesday, Obama called four radio shows to talk about the elections, including a Connecticut program in support of Democratic Gov. Dannel Malloy’s re-election bid against Republican Tom Foley. The president acknowledged the uphill battle his party faced in the Senate.

“This election cycle is probably the worst possible group of states for Democrats since Dwight Eisenhower,” he said. “A lot of states being contested tilt Republican.”

Earnest would not disclose which state residents would be hearing the president’s voice in robocalls or on the radio as voters go to the polls, though Obama also recorded a radio ad on behalf of Sen. Kay Hagan (D-N.C.) in her tough campaign against North Carolina state House speaker Thom Tillis (R).

Alluding to the limits Democratic candidates have put on White House involvement, Earnest said: “The administration and the president have worked closely with the Democratic campaign committees and the individual campaigns to do everything possible to — or at least everything that these candidates believed was in their best interest to advance their candidacies.”

Even before most voters had arrived at their polling sites, GOP leaders were fanning out to project confidence that the party would make good on its promise to turn Election Day into a referendum on the president’s low popularity. Republicans congregated in the green room at MSNBC’s Capitol Hill studio to tout the rebound of the party’s establishment on “Morning Joe.” Before appearances, coffee-sipping players were in good spirits as they compared notes.

Sen. Rob Portman (R-Ohio), vice chairman of the National Republican Senatorial Committee, touted the GOP’s financial success, including the $17 million his group raised last month. Former Mississippi governor Haley Barbour pointed to the primary victory of longtime Sen. Thad Cochran (R-Miss.), who bested a tea-party challenger in June, as a pivotal moment where Republicans avoided nominating gaffe-prone and controversial candidates who could have damaged the party’s appeal.

An optimistic Barbour said he would be on the airwaves for the rest of the day, and then head to a string of election night return-watching parties in Washington — gatherings he expected to be celebrations.

“For us, this is about winning a majority, but it’s also true we’ve got to test whether we are becoming a more competent national party,” Republican National Committee Chairman Reince Priebus said on MSNBC. He said Republicans were intent on appealing to voters’ anger about the direction of the country.

“People see a Washington that isn’t working,” he said, “and the person at the head of it all is the president.”

Democrats fought back, blaming Republicans for standing in the way of their economic agenda.

“People want to feel the ground they’re standing on is a little bit more firm, and the reason they don’t is Republican obstruction,” Debbie Wasserman Schultz, head of the Democratic National Committee, said on MSNBC. “That is the contrast, the choice people are making all across the country.”

Around the country, the parties were making last-minute bids for support.

In the Georgia race for the Senate, Democrat Michelle Nunn, daughter of former senator Sam Nunn (D), visited a campaign office Monday night in suburban Atlanta and was greeted by supporters chanting, “I believe that we will win!” — the same chant used by the U.S. men’s national soccer team at the World Cup last summer.

“Everywhere we go, people are excited, they are energized, and they tell me they are ready to make a change,” she told the crowd.

In Centennial, Colo., Rep. Cory Gardner (R), who is trying to unseat Sen. Mark Udall (D) in a key Senate race, stood on a corner Tuesday morning at a busy intersection, holding a sign that bore his name in large letters.

A gold sport utility vehicle pulled over.

“Hey buddy, how’s it going?” Gardner said as he high-fived a kid who leaned out the window.

“I think I’ve probably waved signs on every one of these four corners over the last 15 years,” he said.

There were honks and cheers, and a man on a bicycle rode by and whooped.

Juliet Eilperin and Peyton Craighill in Washington, Karen Heller in Louisiana, Paul Kane in Kentucky, Ed O’Keefe in Georgia, Wesley Lowery in North Carolina and Katie Zezima in Colorado contributed to this report.