Republicans did not achieve a perfect evening, losing races in several states they had once hoped to win, including the Senate contests in Delaware and Connecticut, because some candidates supported by the Tea Party movement knocked out establishment candidates to win their nominations. But they did score notable victories in some tight races, like Pat Toomey’s Senate run in Pennsylvania.

Senator Reid said in a speech that he was “more determined than ever” after his victory. “I know what it’s like to get back on your feet.”

The outcome on Tuesday was nothing short of a remarkable comeback for Republicans two years after they suffered a crushing defeat in the White House and four years after Democrats swept control of the House and Senate. It places the party back in the driver’s seat in terms of policy, posing new challenges to Mr. Obama as he faces a tough two years in his term, but also for Republicans  led by Mr. Boehner  as he suddenly finds himself in a position of responsibility, rather than being simply the outsider.

In the House, Republicans found victories in most corners of the country, including five seats in Pennsylvania, five in Ohio, at least three in Florida, Illinois and Virginia and two in Georgia. Democrats braced for the prospect of historic defeats, more than the 39 seats the Republicans needed to win control. Republicans reached their majority by taking seats east of the Mississippi even before late results flowed in from farther West.

Throughout the evening, in race after race, Republican challengers defeated Democratic incumbents, despite being at significant fund-raising disadvantages. Republican-oriented independent groups invariably came to the rescue, helping level of the playing field, including in Florida’s 24th Congressional District, in which Sandy Adams defeated Representative Suzanne Kosmas; Virginia’s 9th Congressional District, where Mr. Boucher, a 14-term incumbent, lost to Morgan Griffith; and Texas’s 17th Congressional District, in which Mr. Edwards, who was seeking his 11th term, succumbed to Bill Flores.

Democrats argued that the Republican triumph was far from complete, particularly in the Senate, pointing to the preservation of Mr. Reid and other races. In Delaware, Chris Coons defeated Christine O’Donnell, whose candidacy became a symbol of the unorthodox political candidates swept onto the ballot in Republican primary contests. In West Virginia, Gov. Joe Manchin III, a Democrat, triumphed over an insurgent Republican rival to fill the seat held for a half-century by Senator Robert C. Byrd. And in California, Senator Barbara Boxer overcame a vigorous challenge from Carly Fiorina, a Republican.