Sen. Charles E. Schumer (D-N.Y.), chairman of the Joint Congressional Committee on Inaugural Ceremonies, said the group tries to distribute tickets “evenly and fairly.” (Melina Mara/THE WASHINGTON POST)

They are among the most highly coveted items published by the U.S. Government Printing Office, offering the lucky and usually politically well-connected bearers a chance to witness history.

Tickets. Anybody got one?

President Obama’s second inauguration may not be quite as thrilling as the first, but the official release this week of 250,000 tickets for members of Congress and other government officials to hand out has incited a frenzy on Capitol Hill, with some lawmakers trying to score extras.

“There are many more people who want to come than we have tickets,” said Sen. Charles E. Schumer (D-N.Y.), who chairs the Joint Congressional Committee on Inaugural Ceremonies, which released the color-coded tickets and began distributing them. “But we try to give them out evenly and fairly. From the newest freshman to the highest ranking, each member gets exactly the same number of tickets.”

Still, many lawmakers wonder if they received their fair share and suspect that a colleague may have nabbed more. Neither Schumer nor the committee’s spokesman would say how many tickets each lawmaker gets, though it appears to average at least a couple hundred.

There’s also an inequality of demand. The closer a representative’s district is to Washington, the more intense the jockeying by constituents, and the more likely his or her staff will be bugging other members of Congress for more tickets. And the bugging at times sounds a lot like begging.

Colleagues, constituents, volunteers — some people will try anything.

“Anybody that you’ve ever run across in the business can claim any kind of connection that would ring the bell,” said Kevin Hall, a spokesman for Sen. Mark R. Warner (D-Va.). “At times, people are overly generous about what they’ve done for the boss over the years.”

Politicians in need sometimes go right to the top, pestering congressional leaders — who everyone assumes receive a bigger allotment. Others press lawmakers from distant states or Republican-friendly red states, hoping their constituents are too far away geographically or politically to show much interest in making the trip. But that doesn’t mean it’s easy to scare up extras.

“I think the tickets are so precious that unless you’re really far away, [or] you’re a Republican and you have very few constituents who want to come here, that the tickets are in high demand,” said Rep. Gerald E. Connolly (D-Va.).

His office received requests from 2,100 people, who asked for 10,577 tickets. Connelly has scared up at least two more from a Republican colleague. “And that’s because he represents Utah, where there wasn’t as much demand.”

From the perspective of some red states, the question might even be: What’s all the fuss?

“There are generally enough tickets to go around,” said Rep. Mike Simpson (R-Idaho), who gives his leftovers to his state’s senators or other lawmakers. “It’s not an issue.”

Once tickets are in hand, many members of Congress use lotteries to dole them out to constituents, though at least one California representative started a sort of mini essay contest. Del. Eleanor Holmes Norton (D), who as the District’s nonvoting representative must try to meet some of the largest demand with the least political clout, makes potential ticket recipients promise they will attend, even if the weather is bad.

All the while, the requests keep rolling in from constituents, supporters and campaign volunteers who knocked on doors or worked phone banks. Some skip the Hill and go straight to eBay, where a seller was seeking $1,000 for four tickets to the ceremony. Congressional leaders, infuriated over the scalping, have asked eBay to remove the ads.

“Making a profit off the president’s inauguration on tickets that were meant to be free is unfair,” Norton said.

The tickets come in red, blue, gold and other colors, depending on the level of access. Blue and red tickets get you a seat or a place to stand closest to the ceremony. Yellow means you’ll be standing behind the Capitol Reflecting Pool.

Schumer made sure everyone knew there would be no purple tickets and, hopefully, no repeat of an incident four years ago when a crowd of thousands backed up into the Third Street tunnel, which became known as the “Purple Tunnel of Doom.” Those who were stuck there missed the inaugural ceremony.

Though the fever was highest when Obama made history by becoming the first African American president, planners still expect a big turnout when he takes the oath publicly Monday. (He will take it first in a private ceremony Sunday, Jan. 20, a date required by the Constitution. )

Though not everyone in D.C. wants a ticket to the inauguration, Norton said it feels that way. She fumed that the District would have a lot more to go around if it were represented in Congress like a state. With only about 200 tickets to hand out, she has her staff calling all over the Hill to find more.

“We’ve begged and we’ve pleaded,” Norton said. “You would think, as a booby prize, we would get a few more tickets to the inauguration.”

On Monday, she conducted a lottery to distribute her tickets, with two members of the D.C. National Guard plucking numbers from a basket. Many members of Congress also use lotteries, though some also reserve tickets for donors, volunteers and community leaders. Last time, Connolly put aside a few tickets for the finalists in a charity’s annual youth program and oratorical contest honoring the Rev. Martin Luther King Jr. (This year, the Prince William County contest and the inauguration occur on the same date.)

Rep. Michael M. Honda (D-Calif.) has taken perhaps the most unusual approach, allowing constituents to enter a lottery, join a waiting list or skip both by suggesting ways to make the United States a better place. Staffers combed through the entries posted on the congressman’s Facebook page and picked the best.

William Z. Wilson, a 14-year-old freshman at Stevenson High School in Pebble Beach, Calif., offered ideas for improving the nation’s public schools.

“We could design a program to reward advanced students for giving other students help,” William said in an interview by telephone, with student tutors receiving extra points on their GPAs. He received two tickets.

Kennon Lee, 34, who lives in Rosslyn and works for the State Department, urged Honda to expand the Peace Corps, perhaps by establishing university fellowships or offering tuition assistance in exchange for a tour with the Peace Corps after graduation. He also received two tickets.

Honda said his approach has produced some ideas. But more important, he thinks, it has helped widen his constituents’ access to their representative. Maybe next time, he said, he’ll find a way to help fly the winners to the inauguration.

“Four years ago, we did it, and it was fun, and we thought we would do it again,” Honda said. “A lot of good comes out of it.”

Rosalind S. Helderman contributed to this report.