The senior Republican member of the US Senate, Alaska’s Ted Stevens, conceded defeat Wednesday in his race for a new term.

The announcement by Stevens confirmed that Democrats will have at least 58 seats in the new Senate. And with two contests yet to be settled — in Minnesota and Georgia — the party that just two years ago was a minority player in the chamber could begin the new Congress with a filibuster-proof majority of 60.

While several thousand ballots are still to be reviewed in Alaska, Stevens acknowledged Wednesday that he fallen so far behind Democratic challenger Mark Begich that his reelection was now out of the question.

“Given the number of ballots that remain to be counted, it is apparent the election has been decided and Mayor Begich has been elected,” said Stevens, who campaigned for a new term despite having been convicted prior to the election on seven felony counts of hiding illegal gifts from an Alaskan contractor.

Republicans had hoped Stevens would be reelected and that he would then be expelled from the Senate or forced to resign — a circumstance that would position an Alaskan Republican, perhaps Governor Sarah Palin, the party’s 2008 vice-presidential candidate, to claim the seat in a 2009 special election.

But it was not to be.

After a long day of counting in Alaska Tuesday, Begich led by 3,724 votes. The Associated Press labeled this “an insurmountable lead, with only about 2,500 overseas ballots left to be counted” and identified the Democrat as the winner.

Steven’s concession confirms that Begich, the mayor of Anchorage, will now be the 58th member of the Senate Democratic Caucus. (That’s 56 Democrats, Vermont Independent Bernie Sanders and Connecticut Independent Joe Lieberman — who on Tuesday was effectively welcomed back into the caucus by members who allowed the backer of Republican John McCain to retain his chairmanship of the powerful Homeland Security Committee.)

Could Democrats make it to 60 seats, thus positioning the party to override Republican procedural moves to block legislation and approve Obama administration nominations?

In a word: Yes.

Democrat Al Franken is still locked in a Minnesota recount fight with Republican Senator Norm Coleman. If Franken wins, as is very possible, that would be seat 59.

Democrat Jim Martin gets another shot at Republican Senator Saxby Chambliss in Georgia. If Martin wins that uphill but doable race, that would be seat 60.

Democrats went into the 2008 competition with a 51-49 split in the Senate.

Democratic candidates took seats where Republican incumbents were stepping down in Colorado, New Mexico and Virginia. And they beat Republican incumbents in New Hampshire, North Carolina, Oregon and, now, Alaska.

The Stevens defeat is a sweet one for Democrats, who had expected to displace the convicted senator with relative ease on November 4 but instead saw the felon pull ahead in the initial tabulations. Begich caught up only as as early votes and so-called “questioned ballots” were counted.

Begich’s win is good news for Senate Democrats and, at least to some extent, for Senate Republicans, who will now be relieved of the burden of kicking Stevens out of their caucus. But that caucus is small, and getting smaller.