WASHINGTON – Despite a bitterly and closely fought presidential campaign fueled by record financial backing, analysts sifting through Tuesday’s national election results here are forecasting a period of introspection for the opposition Republican Party that could ease the gridlock that has gummed up Washington politics in recent years.

Of particular interest will be signs of accommodation ahead of critical negotiations, to start almost immediately, on how to deal with the country’s mounting debt. Without a broad deal between Democrats and Republicans, a series of tax increases and spending cuts are set to go into effect in January that economists are warning could send the fragile U.S. economic recovery back into recession.

President Barack Obama will now go into those negotiations significantly strengthened. On Tuesday, voters not only rewarded Obama with a larger than expected victory, but the president’s Democratic Party did far better than anticipated in races for the U.S. Senate, where Republicans had hoped to wrest control.

Many now suggest those hopes were dashed largely because of Republican overreach in nominating overly conservative candidates in key battleground races. More broadly, however, the surprisingly strong turnout for the Democratic Party is being seen as a repudiation of the grinding refusal by Republicans to work with President Obama on nearly any legislative issue over recent years.

“Republicans have been unwilling to compromise, and now we have to allow for a period in which Republicans have to find their party’s soul,” Isabel V. Sawhill, co-director of the Center on Children and Families, here in Washington, said Wednesday. “They’re a divided party right now, but there are still moderate Republicans – if not in the House, then out there in the country – who are not happy with where the Republicans are right now.”

Sawhill warns that this period of introspection will be “messy,” however, and will most likely start with a divisive blame game over the party’s poor electoral showing, which saw a surprising strengthening by Democrats in the Senate. Republicans continue to hold the House of Representatives, though, and have already begun staking out their positions ahead of the debt negotiations.

The conservative “Tea Party” faction of the Republican Party, initially a reaction to debt concerns but more recently seen as a new incarnation of the religious right, has gone on the offensive ahead of expected backlash that its influence had a negative impact on the Republican Party’s electoral chances. Two prominent Tea Party candidates were voted out of power on Tuesday, while a third is narrowly leading a race that may go to a recount.

Despite this poor showing, the Tea Party Patriots, the country’s largest such group, has launched an attack on the Republican establishment for “hand-picking a weak … elite candidate who failed to campaign forcefully on America’s founding principles – and lost.”

According to Jenny Beth Martin, the group’s national coordinator, the Tea Party will now renew its efforts. “Our work begins again today,” she said in a statement Wednesday. “We will turn our attention back to Congress, to fight the battles that lie ahead.”

“No consensus between the parties is in sight after the election, and polarization has been exacerbated, not diminished,” Thomas Mann, a noted congressional scholar with the Brookings Institution, a Washington think tank, told journalists Wednesday morning. “Nonetheless, the president has some opportunities for breaking through the gridlock … party because some Senate Republicans are tired of simply obstructing whatever the president proposes.”

Mann noted that “voters have done their job by … punishing the Republicans for their reckless obstruction.”

Not only have voters spoken relatively clearly, but far more of the country likewise reportedly supports President Obama’s agenda. As noted in a new article by Mark Weisbrot, co-director of the Center for Economic and Policy Research, a Washington think tank, “the country is nowhere near as closely divided as the popular vote indicates … non-voters, who were about 43 percent of the electorate in 2008, favor Obama by a margin of about 2.5 to one.”

Yet first scared of Obama’s sudden rise to power and second angered over his forceful passage of health-care reform, Republican leaders in both wings of the U.S. Congress in recent years have made stymieing legislative progress – and blaming Obama for the deadlock – a central political strategy.

While the election results will be widely seen as a mandate for the president and a repudiation of Republican stonewalling, initial public reactions by the Republican leadership suggested a doubling down.

Following the election results, Senate Republican minority leader Mitch McConnell, seen as the architect of the “no cooperation” tactic, warned President Obama that he would need to move towards Republican positioning if he hoped to get any major legislation passed during his second term.

John Boehner, the leader of the House of Representatives, likewise noted Tuesday night that the House had been “the primary line of defense” against government spending and forcefully highlighted that voters had “responded by renewing our House Republican majority.”

Still, there are already signs of softening and self-reflection on the right, and by Wednesday afternoon Boehner was already sounding a far more cautious note. In a major address on his positions ahead of the debt negotiations, he called for Democrats and Republicans to find “the common ground that has eluded us”.

“My message today is not one of confrontation,” Boehner said. “I’m not suggesting we compromise on principles, but rather that we commit to creating an atmosphere in which we can find common ground – and seize it.”

The chair of the National Republican Senatorial Committee, Senator John Cornyn, has gone still farther.

“It’s clear that with our losses … we have a period of reflection and recalibration ahead for the Republican Party,” he stated immediately after the election results were announced.” While some will want to blame one wing of the party over the other, the reality is candidates from all corners of (the party) lost tonight. Clearly we have work to do in the weeks and months ahead.”

According to some, part of that work needs to include a rethink on today’s political infrastructure in the United States, particularly the “primary” process that selects candidates in the first place, which may be forcing Republicans towards more extreme positions.

“In the U.S. today, polarization is structural,” Jonathan Rauch, a guest scholar with the Brookings Institution, said Wednesday. “Members of Congress are worried about their own campaigns over national issues – no one gets punished for standing their ground, they get punished for compromise. I think we have to start talking about changing the primary process, because without moderate candidates there will be no moderate voters.”