One of Mayor Bloomberg’s Republican challengers, Steven Shaw, told The New York Sun yesterday he would be dropping out of the race this week and throwing his support to Mr. Bloomberg’s other GOP opponent, Thomas Ognibene.

Mr. Ognibene, however, expressed serious concern about getting onto the primary ballot and advocated a change in the city’s ballot-access rules to allow for more spirited competition among Republicans.

With only four days left in the petitioning phase of the campaign, Mr. Shaw, an investment banker who lives in Brooklyn, said he has gathered fewer than 2,500 signatures from registered Republicans on petitions asking that he be placed on the ballot for the September 13 primary.

To qualify for the Republican contest, a candidate needs 7,500 valid signatures.

“The likelihood is that I’m not going to be making the ballot,” Mr. Shaw said. “I gave it all I had, and I’m going to be sending out an announcement sometime this week,” to announce his withdrawal from the race, he added.

Mr.Shaw, 30, entered the mayoral race in June 2004, decrying the tax hikes and what he characterized as profligate spending, lack of job growth, and hostility to business that materialized in the city under Mr. Bloomberg’s governance. Mr. Shaw was the first candidate to pose a challenge to the mayor from the right in this year’s race, accusing Mr. Bloomberg, a lifelong Democrat, of failing to uphold the banner of the limited government, free-market principles that he said define the Republican Party.

Mr. Shaw said he had gathered 600 of his petition signatures himself and in the process knocked on about 3,000 doors, speaking with city Republicans about their views of Mr. Bloomberg and the state of the city and the party. Many New Yorkers, Mr. Shaw said, share his concerns about the mayor but do not necessarily want to work for, or contribute money to, Mr. Bloomberg’s more conservative opponents.

Most of his signatures, Mr. Shaw said, came from Staten Island and Brooklyn, and in his interactions with outer-borough Republicans, he said, he found very few who shared his fiscal conservatism.

“They’re mainly kind of national-defense Republicans,” Mr. Shaw said, “and most of the ones who are policemen and firemen often have a background in the military.”

“It’s not as if something such as taxes, or budget reform, is an issue anywhere near the top of the radar screen,” Mr. Shaw said. “They mainly want a contract.” The Bloomberg administration’s labor negotiations with uniformed public employees and teachers have dragged on unproductively.

The mayor’s abundant resources, Mr. Shaw said, also posed an obstacle, particularly Mr. Bloomberg’s huge cohort of “paid volunteers,” who far outnumber the other campaigns’ petition-gatherers.

“He’s able to do things neither Tom nor I are able to do,” Mr. Shaw said. “Money talks.”

Mr. Shaw said he raised and spent around $36,000 on his campaign, $25,000 of it from his personal coffers. Mr. Bloomberg, a multibillionaire, is expected to spend $100 million or more on his re-election.

Mr. Shaw said he would vote for Mr. Ognibene.

“I think Tom is a great candidate,” Mr. Shaw said. “I think he’s worked extremely hard for the city and the Republican Party for a long time, and I’ll do everything I can to support his campaign.”

Mr. Shaw said he would “definitely encourage” his own team to help Mr. Ognibene’s efforts.

“It’s a question of ‘do you want someone as liberal as any of the Democratic candidates – Mayor Bloomberg – or do you want someone who’s a Republican to represent the Republican Party?'” Mr. Shaw said.

As of yesterday, however, Mr. Ognibene lacked the requisite signatures to vie for the Republican nomination in September. The former City Council minority leader from Middle Village, Queens, said his campaign had gathered around 6,000 petition signatures. To obtain the remaining 1,500, Mr. Ognibene said, his campaign enclosed, in mailings sent to around 10,000 two-Republican households, ballot petitions to be signed, witnessed, and returned, and followed up with a “canned” phone message from the candidate.

Even if the U.S. Postal Service delivers Mr. Ognibene’s outstanding petitions by Thursday’s deadline, however, the campaign will fall far short of the 15,000 signatures Mr. Ognibene hoped to get to build a comfortable buffer against signature challenges from the Bloomberg campaign. Mr. Ognibene said he, like Mr. Shaw, had found it surprisingly difficult to gain Republican signatures, and largely blamed Mr. Bloomberg’s superior resources.

“The mayor flooded my popularity area,” Mr. Ognibene said, referring to the blitz of paid Bloomberg volunteers who, he said, “soaked up” Republican signatures in the challenger’s former City Council district.

“There’s only so much money I had,” Mr. Ognibene lamented.

Mr. Ognibene said he has enough money, however, to remain a gadfly to the mayor as he seeks re-election. The former councilman – who, in addition to echoing Mr. Shaw’s concerns about Mr. Bloomberg’s spending and tax hikes, is a social conservative opposed to abortion rights and same-sex marriage – has pledged to run on the Conservative Party line through to the general election in November. Moreover, he said he would raise the $50,000 he needs to qualify for participation in the mayoral debates, having acquired between $47,000 and $48,000 in qualifying contributions. Mr. Ognibene has until September to come up with the rest.

“If I can get into the primary with the mayor,” Mr. Ognibene said, “it’s going to be a lot closer than people think. But if I have to run on the Conservative Party line, I still have an important mission.”

That mission, Mr. Ognibene said, will be in the Conservative Party tradition of acting as the Republican Party’s conscience. Indeed, a veteran city political consultant, Jerry Skurnik, said Mr. Ognibene stood to do the most damage to Mr. Bloomberg as a Conservative Party candidate in the general election. In a close contest in November, Mr. Skurnik said, Mr. Ognibene could play spoiler if he pulls more than 50,000 votes – Mr. Bloomberg’s margin of victory in 2001.

Mr. Ognibene also faulted the city’s restrictive ballot-access rules for the difficulties encountered by his campaign, and he recommended reducing the signature requirement to 3,500.

In citywide elections, a candidate must receive either 7,500 signatures or the equivalent of 5% of the party’s enrollment to appear on a primary ballot, Mr. Skurnik said. The 5% provision works to the benefit of smaller third parties, giving them lower thresholds for putting candidates into primary contests. Requiring the same number of signatures for Republicans and Democrats, however, creates a stifling environment for grassroots Republican candidates, Mr. Ognibene said.

Because Democrats outnumber Republicans by at least five to one in the city, Mr. Skurnik said, most candidates can conduct effective street-corner petitioning and get on the Democratic primary ballot with little effort.

According to a longtime Republican activist, Robert Hornak, that makes for livelier campaigns on the Democratic side, where the open exchange of ideas that takes place in a primary helps build the party. Because it can be harder for Republicans to force a primary, the GOP lacks that opportunity for such revitalization. That is exacerbated by the fact that “the Republican Party is too authoritarian by nature,” Mr. Hornak said, describing the organization as top-down, personality-driven, and hostile to grass roots campaigns.

As for Mr. Bloomberg, Mr. Hornak said the mayor “should be embracing a primary” for the good of the city’s GOP.

“The only reason I can imagine he’d be afraid of one is if he stood a chance of losing,” Mr. Hornak said.

Mr. Skurnik, however, saw a different motivation. “As soon as word got out that he might have a problem with the Republican primary, he went all-out to make sure to get people back on the reservation,” Mr. Skurnik said of the mayor. “It shows the campaign is not taking anything for granted.”