* Democrats eke out narrow victories in two Republican states
* Both parties start to dig in on fiscal cliff negotiations
* More polarized replacements for moderate Democrats, Republicans
By David Lawder
WASHINGTON, Nov 7 (Reuters) - Democrats defied the odds to increase their thin majority in the U.S. Senate by two seats on Wednesday, eking out narrow victories in Republican-leaning Montana and North Dakota.
Jon Tester, who had been considered one of the Democrats' most vulnerable senators in Tuesday's election and a key takeover target for Republicans in Montana, defeated Representative Denny Rehberg by a 48.8 percent to 44.7 percent margin. Libertarian candidate Dan Cox siphoned off 6.5 percent of the vote.
In North Dakota, Republican candidate Rick Berg conceded the final Senate race on Wednesday afternoon to Democrat Heidi Heitkamp, who held on to a razor-thin lead of fewer than 3,000 votes, which had qualified for a recount.
The two wins give the Democrats a 55-45 Senate majority - including the expected support of two independent senators - compared with 53-47 currently.
The shift slightly strengthens the hand of Senate Majority Leader Harry Reid in the chamber, where significant legislation often requires 60 votes to move forward.
Reid told a news conference he wants to reform Senate rules to make it easier to pass legislation with a simple Democratic majority, but said he was willing to negotiate with Republicans "any time, any issue."
As Congress pivots to deal with the year-end "fiscal cliff" of expiring tax cuts and the launch of automatic spending cuts, Reid also underscored some areas on which he is less willing to compromise in a deficit-reduction deal.
"We are not going to mess with Social Security," he said, repeating a Democratic campaign pledge to protect seniors' retirement and health-care benefits.
Many political pundits had thought Democrats would do well to barely hang onto Senate control in Tuesday's election, losing one or two seats in the process. However, in addition to Tester's seat in Montana, they successfully defended seats considered vulnerable in Missouri, Virginia and Connecticut and wrested seats away from Republicans in Massachusetts and Indiana.
The Republican setback was in part self-inflicted, the result of internal battles waged in the party and controversial comments about rape and abortion.
Had conservative Republican Richard Mourdock not defeated veteran moderate Richard Lugar in Indiana's primary, for example, that seat might have stayed in Republican hands instead of being won by Democrat Joe Donnelly on Tuesday.
Missouri Senator Claire McCaskill, who kept her seat on Tuesday, was considered unlikely to win in the conservative state until Representative Todd Akin won the state's Republican primary.
Akin and Mourdock stumbled badly with remarks about abortion that were widely criticized as unsympathetic to rape victims, handing Senate Democrats two of Tuesday's biggest wins.
The election left the Senate somewhat more polarized, with generally fewer moderates and more conservatives among the Republicans and more liberals among the Democrats.
Republicans remained firmly in control of the House of Representatives, ensuring that Congress still faces a deep partisan divide in deficit-reduction talks aimed at replacing automatic spending cuts and determining future tax rates.
With President Barack Obama retaining the White House, the status-quo result portends more partisan gridlock.
"That means the same dynamic. That means the same people who couldn't figure out how to cut deals for the past three years," said Ethan Siegel, an analyst who tracks Washington politics for institutional investors.
Republicans managed to flip one Democratic Senate seat, in Nebraska, where conservative candidate Deb Fischer, endorsed by former Republican vice presidential candidate Sarah Palin, defeated former Democratic governor Bob Kerrey in the race for the seat of retiring Democrat Ben Nelson.
Two victories underscored the Senate's shift away from moderates who are more able to find common ground.
Elizabeth Warren, the winner over moderate Senator Scott Brown in Massachusetts, is a consumer activist and Harvard Law School professor unpopular with Wall Street. In a victory speech, she vowed to "hold the big guys accountable."
"To all the seniors who deserve to retire with the security they earned, we're going to make sure your Social Security benefits are protected and that millionaires and billionaires pay their fair share," Warren told supporters.
In Texas, the seat of a retiring Republican, Kay Bailey Hutchison, was filled in an easy victory by Republican Ted Cruz, also a favorite of the Tea Party.
As Congress starts this week to seek a way to deal with the year-end expiration of Bush-era tax cuts and the launch of automatic spending cuts, the results point to a continued bitter divide.
Republican House Speaker John Boehner said voters wanted to continue the Republicans' agenda, but pledged to work "with any willing partner."
"With this vote, the American people also made clear there's no mandate for raising tax rates," Boehner told party activists in Washington.
With Obama's re-election and the Democratic Party retaining a m ajority in the Senate, Democrats are expected to be emboldened in pushing their plan for tax fairness - cutting budget deficits by asking wealthy Americans to pay higher tax rates, while extending lower rates for the middle class.
But less than two months remain before tax cuts enacted under President George W. Bush expire on Dec. 31, thrusting higher rates on all Americans. Two days later, $109 billion in across-the-board spending cuts begin to bite. If unchecked by Congress, the fiscal cliff would suck some $600 billion out of the U.S. economy next year.
Top Senate Republican McConnell, who will face tougher bargaining on the Democratic side, said voters simply gave Obama "more time" to fix the country's problems. Putting a brave face on the results, he called on the president to work with Republicans on the fiscal cliff and tax reform.
"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.