WASHINGTON  When Mark Begich, the popular 45-year-old mayor of Anchorage, came to town for a meeting of mayors in January, he was beckoned to the Capitol by the Senate majority leader, Harry Reid of Nevada. There was one agenda item: ousting Senator Ted Stevens of Alaska, the senior Republican in Congress.

For 45 minutes, Mr. Reid and Senator Charles E. Schumer of New York, the head of the Democrats’ campaign efforts, pressed the mayor to run this year. Last week, they got him. Mr. Begich announced that he had formed a committee to start raising money. Effectively, the race is on.

For Democrats hoping the November elections set off a seismic shift in Washington, the dream scenario is not just capturing the White House, but also winning a filibuster-proof majority of 60 seats in the Senate  a luxury no president has enjoyed since Jimmy Carter 30 years ago.

As far-fetched as that might seem  Democrats now control the Senate by a razor-thin 51 to 49, thanks only to two independents who vote with them  some Democrats have started thinking aloud that such a scenario is within reach.