BOSTON — In the universe of House candidates, they’re not the sure things, nor are they the long shots. They’re the ones in between — and they were all over the Democratic National Convention last week.

For otherwise-attractive Democratic candidates who face long odds by running against a GOP incumbent or in a Republican-leaning district, last week’s convention offered the best chance yet to audition for, and network with, the fundraisers and party honchos who have the power to make or break their campaigns in November.

“Any serious candidate running for the Senate or the House would be here,” said businesswoman Christine Jennings, who is seeking the Democratic nomination to challenge Rep. Katherine Harris (R-Fla.) in the fall. “This is one of the biggest events that happens in political life.”

Kori Bernards, communications director for the Democratic Congressional Campaign Committee, said there is no “set policy” the organization offered to candidates seeking advice about whether to attend the convention.

“Generally we have been in favor of candidates coming up who could benefit from it,” said Bernards in an interview late last week. “But, there is an argument to be made that candidates’ time would be better spent raising money in their districts.”

Jane Mitakides, a first-time candidate in Ohio’s 3rd district, is a good example of a mid-tier candidate who came to Boston in hopes of boosting her prospects.

The fact that Mitakides is running against an incumbent — freshman Republican Michael Turner — and in a district that was tipped slightly Republican by redistricting in 2002 has left her off the top-tier lists compiled by independent handicappers and, more important, the DCCC, whose financial coffers have the power to push her into “real contender” status.

But the 55-year-old communications professional and small-businesswoman also has some advantages to tout. Her opponent is not a firmly ensconced incumbent, having won his seat in a late-developing race after long-serving Rep. Tony Hall (D-Ohio) was appointed to a job with the United Nations in 2002.

Most importantly, Mitakides argues, Ohio is a crucial battleground in the race for president this fall. Since her contest is one of only one of two House races in the state that is even theoretically competitive, aiding her campaign could pay dividends in turnout and grassroots excitement for the Democratic nominee, Sen. John Kerry (Mass.), she contends.

Making the case for bumping her race up to “target list” status was the primary reason Mitakides came to Boston. She likens it to a job interview, in which the prospective employer knows the facts but has tough questions to ask before signing the deal.

“It’s been nonstop activity,” she said in an interview Thursday at the Ohio delegation’s area on the convention floor. “This is a wonderful opportunity to have the main Democratic organizations and interests gathered all in one place. I’ve been trying to reach out and introduce myself to as many people as possible.”

In Boston, Mitakides met with the DCCC chairman, Rep. Robert Matsui (Calif.), and with House Minority Leader Nancy Pelosi (Calif.).

The high point for her was the Ohio delegation breakfast on Thursday, when she was asked to address the crowd along with such luminaries as former Ohio Sen. John Glenn (D), and Sen. John Edwards (N.C.), the Democrats’ just-anointed vice presidential nominee.

The convention experience, Mitakides said, “has so exceeded my expectations. I can say from the heart that I have accomplished more each day than I had hoped to do in a week.”

That said, she — and most other mid-tier candidates — came away from Boston without a firm agreement to have the campaign bumped up to a targeted race.

But, according to Jennings, promises of support are less important than the symbolism conveyed to party regulars by her attendance.

“Coming here to me showed how serious you are,” she said.

Jennings is currently embroiled in four-way Democratic primary, with the main competition provided by 2002 nominee Jan Schneider, who also attended the festivities in Boston.

If she wins, Jennings argued, the general election contest will “definitely be one of the top-five races in the nation.”

That prediction may be a bit far-fetched given the Republican tilt of this Sun Coast seat and Harris’ massive war chest. Harris endeared herself to Republicans nationwide after her actions as Florida secretary of state helped deliver contested electoral votes to George W. Bush in 2000.

Harris had $1.2 million in the bank at the end of last month. Jennings had $438,000 on hand, a total that included a $300,000 personal donation.

While Mitakides and Jennings offer examples of candidates hoping that the convention catapulted them into the DCCC’s top tier, many others attended the gathering hoping mainly to attract some momentum and attention to their campaigns.

One of these is Tim Sultan, who’s challenging Rep. Jim Kolbe (R) in the southern Arizona 8th district.

Sultan has relied on a web of colleagues, built during his days as an aide to then-Sen. Dennis DeConcini (D-Ariz.) and Pelosi, to make his time in Boston worthwhile.

Sultan met with DCCC officials, House Members such as Rep. Jim Turner (Texas) and even had a conversation with former President Bill Clinton.

“The convention was absolutely the best thing I could have done with my time,” Sultan said. “My goal was to get national support for a race that had never been targeted in the past.” And on that front, Sultan said, he considered the task “mission accomplished.”

Bob Derry (D), a retired banker challenging House Appropriations Chairman Bill Young (R-Fla.), acknowledged that he had a more mixed experience.

“I am a political amateur in the purest sense of the word,” said Derry when asked why he decided to come to Boston. “I have no name recognition and don’t know the ‘powers that be.’ I came up with the hope of meeting some of them.”

On its face, the St. Petersburg-based 10th district is extremely competitive between the parties — Al Gore won the district with 51 percent in 2000 — but Young has had little trouble holding it for the past 34 years, as most constituents seem to appreciate his powerful Appropriations post.

Derry has struggled to raise money, reporting just $12,000 in the bank at the end of June.

Derry said that in his time in Boston he had “made some inroads and some contact with fundraisers that I would not ordinarily have a chance to meet.”

But, he admitted, that he had “not done as well as I hoped, but better than some might have projected.”