Washington (CNN) -- 2010 has opened on an unsettling note for Democrats in the U.S. Senate.

Connecticut's Chris Dodd and North Dakota's Byron Dorgan -- two longtime power players in the chamber -- have announced their intention to step down at the end of the year. If history is any guide, the party now faces an uphill struggle to maintain its 60-seat supermajority.

Failure to do so could have serious ramifications for President Obama as he tries to look past the health care debate and tackle global warming, ballooning budget deficits and a range of other politically contentious issues.

The fight over health care reform has clearly demonstrated that 60 votes is now the minimum threshold for passing major legislation through the Senate. Anything less leaves the majority party at the mercy of a minority increasingly willing to employ the filibuster to grind the legislative gears of the Senate to a halt.

Democrats currently have exactly 60 members in their caucus; Republicans have 40. The GOP knows that presidents typically lose House and Senate seats during midterm elections, and is banking on that fact to block much of Obama's agenda.

"Midterm elections are usually low-turnout affairs," noted CNN polling director Keating Holland. "Conservative Republicans, however, have been energized by their strong opposition to Obama's agenda. They're likely to vote this November. Many liberals, on the other hand, don't feel Obama has pushed strong enough on their issues. It's unclear at the moment if they'll be as likely to show at the polls."

This year, Democrats must defend 19 seats, including an opening that occurred when veteran Massachusetts Sen. Ted Kennedy died. A special election for Kennedy's seat -- widely expected to be won by the Democrats -- will take place January 19.

Republicans are defending 18 seats.

The GOP, according to many analysts, is now placing a high priority on picking up Democratic seats in Colorado, Delaware, Illinois, Nevada, North Dakota and Pennsylvania.

The Illinois and Delaware seats were once held by Obama and Vice President Joe Biden, respectively. Obama's replacement, Sen. Roland Burris, was immediately tainted after being tapped to fill Obama's vacancy by Rod Blagojevich, the state's scandal-plagued former governor. Burris is not seeking election in his own right.

Biden's replacement, Sen. Ted Kaufman, is likely to step aside in favor of the vice president's son, Delaware Attorney General Beau Biden, analysts believe. Delaware's longtime GOP congressman, Mike Castle, is being touted as the likely Republican nominee.

Senate Majority Leader Harry Reid, D-Nevada, is struggling to manage Obama's more progressive agenda while also seeking a fifth term from his traditionally conservative state. Republicans, however, are having a tough time unifying behind an opponent.

At the same time, five-term Pennsylvania Sen. Arlen Specter remains a high-profile target for conservatives enraged by his decision to switch from the Republican Party to the Democratic Party last year. Before he can get to the general election, Specter will face a tough primary challenge from Rep. Joe Sestak, a former admiral.

Also in the GOP's crosshairs is two-term Arkansas Democrat Blanche Lincoln, who recently cast a tough political vote in favor of Reid's health care bill.

Dodd's decision to retire, however, is widely believed to be beneficial to Democratic chances in largely liberal Connecticut. The state's popular Democratic attorney general, Richard Blumenthal, declared his candidacy a few hours after Dodd announced he was stepping down.

Democratic leaders, for their part, are placing a high priority on picking up GOP seats in Kentucky, Missouri, New Hampshire, and Ohio. Republicans have been stung by incumbents' decisions to retire in all four states.

Louisiana, a more conservative state, has attracted the interest of Democratic strategists. First-term GOP Sen. David Vitter has been tarred by his 2007 admission that he had a relationship with a prostitute.

This year's race in Florida has also become an increasingly high-profile contest, largely due to Republican infighting. GOP Sen. George LeMieux, who was appointed to the Senate after former Sen. Mel Martinez unexpectedly stepped down last year, is not seeking a full term.

The state's GOP governor, Charlie Crist, was widely expected to take the seat, but is now facing an unexpectedly strong conservative primary challenge from former Florida House Speaker Marco Rubio.

Republicans are still, however, favored to hold the seat.

CNN's Mark Preston and Paul Steinhauser contributed to this report.