Democrats on Wednesday strengthened their control of the U.S. Senate by pulling off an upset win in the conservative state of North Dakota, a final blow to Republicans who had once been favored to take control of the chamber.

The North Dakota race was the last to be called of Tuesday's 33 Senate contests. With it, Democrats increased their advantage in the chamber by two, to 55-45, counting two independents expected to align with them.

But newly re-elected President Barack Obama must still contend with a divided Congress _ and the potential for more political gridlock _ since Republicans kept their solid majority in the House of Representatives.

The numbers in both chambers were largely unchanged after Tuesday's vote. But the new Congress will be more diverse, with a record 20 women winning Senate seats, including two Democrats who will be the first openly gay senator and the first female Asian-American senator. A record number of Latinos will serve in the House.

Democrats prevailed in two close races in conservative western states. In North Dakota, former state attorney general Heidi Heitkamp won a surprise victory over a heavily favored Republican congressman in a bid for a seat being vacated by a retiring Democrat. In Montana, Sen. Jon Tester, who narrowly won his seat when Democrats captured the Senate in 2006, was re-elected.

Republicans hurt their chances of winning the Senate when candidates in Missouri and Indiana _ both states won by Republican presidential nominee Mitt Romney _ made damaging comments about rape and abortion and went on to lose. An incumbent Republican fell in liberal Massachusetts, while Republicans also lost a seat in Maine.

Only a dozen or so Senate races out of the 33 on the ballot had been seen as competitive. Throughout Tuesday night and into Wednesday, one after another was won by Democrats. Republicans, though, picked up a Democratic-held seat in Nebraska and fended off strong challengers in Nevada and Arizona.

Control of the Senate virtually ensures that Obama's signature legislative achievement, his health care overhaul, will be fully implemented in 2014. Republicans had promised to repeal it.

More than $2 billion was spent on the nasty fight for Congress. All 435 House seats were on the ballot, and Republicans retained control there, though Democrats made a few gains. With most races decided, the new House looked like it would resemble the current one, which Republicans control by 240-190, with five vacancies.

While Republican Rep. Paul Ryan lost the vice presidency, he did win another term to his Wisconsin House seat.

House Speaker John Boehner, who gets to keep his job, offered to work with both parties in Congress. But Boehner also said that by keeping Republicans in control of the House, voters made clear there is no mandate for raising taxes. Obama has proposed ending Bush-era tax cuts for households earning over $250,000 a year.

The first post-election test of wills could start next week, when Congress returns from its election recess to deal with unfinished business _ including the looming so-called fiscal cliff of $800 billion in tax increases and automatic spending cuts to take effect in January if Congress doesn't come up with a compromise to head them off. Economists warn that failure to reach a deal could plunge the U.S. back into a recession.

Newly elected Elizabeth Warren, a Massachusetts Democrat who won a marquee race against incumbent Scott Brown, said Wednesday she believes there is a "lot of room for compromise." Warren, a favorite among liberals as a leading consumer advocate, told NBC's "Today" that Congress can find a middle ground to bring down the deficit by cutting spending while raising revenues.

Democrats began the year in a precarious position, defending 23 Senate seats and losing several retiring veterans in Republican-leaning states, all while voter discontent lingered over the sluggish economy and Obama's health care overhaul. But the Democrats fielded some strong candidates, and Republican prospects were undermined by some candidates who apparently proved to be too conservative and by the surprise retirement of Sen. Olympia Snowe in Maine. Independent Angus King, a former governor, won a three-way race to replace her.

King has vowed to be a bridge between the parties and has not said whether he would caucus with the Democrats or Republicans. However, he was expected to side with the Democrats after Republican groups spent hundreds of thousands of dollars on ads attacking him.

Senators who rode the Democratic wave in 2006 were elected to second terms in Ohio and Pennsylvania. In Virginia, Tim Kaine, a former governor and Democratic national party chairman, won a costly, close race.

In Connecticut, a Democrat won a seat that Republicans had once hoped would be captured by Linda McMahon, the former head of World Wrestling Entertainment who spent more than $42 million of her own fortune in the race.

Women made big gains in the Senate. Democratic congresswoman Tammy Baldwin won in Wisconsin and will become the first openly gay senator. Democratic congresswoman Mazie Hirono of Hawaii becomes the first Asian-American woman to serve in the Senate.

In New Hampshire, wins by two Democrats in House races gives the state, which has two women senators, an all-female delegation to Congress, along with a newly elected woman as governor.

Congress almost got its first black Republican woman, but Mia Love lost a close House in Utah.

A record number of Latin-American congressional candidates ran, according to the National Association for Latino Elected and Appointed Officials, and the House will have several new Latino members.

Republican Ted Cruz, the son of a Cuban-born father and a tea party darling, won a Senate race in Texas. Republican Deb Fischer, another tea party favorite, won in Nebraska.

Republicans also did well in the Southwest. Arizona congressman Jeff Flake won a tough race to hold a Republican seat and Nevada Republican Sen. Dean Heller turned back a strong challenge.

While Democrats will increase their margin in the Senate, they will remain below the 60-vote supermajority needed to easily pass legislation under Senate rules.

Senate Minority Leader Mitch McConnell offered to work with the Democrats and Obama if the president is ready to compromise.

"To the extent he wants to move to the political center, which is where the work gets done in a divided government, we'll be there to meet him half way," McConnell said.

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Associated Press writers Donna Cassata contributed to this report from Washington.