Rep. Doug Ose (R-Calif.) reiterated Tuesday that he will decide by the end of May whether he will challenge Sen. Barbara Boxer (D) in 2004. But Republican strategists on both coasts said they believe the lawmaker from Sacramento will make the race.

If he runs, Ose would be the first major challenger in a race that so far has featured a smorgasbord of possible Republican names but no official candidates. While there is some debate about whether Boxer really is vulnerable, most Republicans agree that Senate hopefuls will need to make their decisions relatively early in order to get a head start in raising money for what will likely be a prohibitively expensive race.

Ose, who is in his third term in the House, formed an exploratory committee in December and, officially, has not yet made up his mind about whether he will run. He said as much in a brief interview Tuesday. But unofficially, GOP officials believe he is a strong bet to run.

“He’s putting things in place in a methodical fashion,” said a Washington Republican strategist, adding that Ose’s planning has advanced far beyond that of the other candidates considering a run.

In late 2002, Ose’s longtime chief of staff, Marko Mlikotin, left the lawmaker’s D.C. office to head up his district operation. Earlier this month, Mlikotin came off the federal payroll, taking a leave of absence from the Congressional job to work full time for the exploratory committee.

“California Republicans are telling the Congressman that Boxer’s record … makes her vulnerable, and they believe he should run in 2004,” Mlikotin said.

Ose has also hired as a general consultant Sacramento-based operative Tony Russo, whose most recent major client was new Hawaii Gov. Linda Lingle (R), the first Republican to win a gubernatorial race there since 1962.

Ose has had conversations with the National Republican Senatorial Committee about the race, and in recent weeks he has been traveling all over California making contacts with potential donors.

“My sense is that he’s talking to the full spectrum of the donor community,” said a California GOP operative. “He’s been making the rounds quite thoroughly.”

One big factor Republicans will be watching to determine Ose’s viability is the size of his checkbook and the extent to which he could self-fund his campaign.

As of September 2002, Roll Call had Ose at No. 11 on its annual list of the 50 richest Members of Congress. At that point, his estimated net worth was $50 million, most of it from the family commercial real estate business and a company he started that specializes in mini-storage facilities.

What is not clear is how much of Ose’s fortune is liquid and thus available for him to pour into his campaign coffers. Most Golden State observers believe a candidate would need at least $20 million to run a viable Senate campaign. In 1998, then-state Treasurer Matt Fong (R) spent $10.7 million in his bid to unseat Boxer, who spent $13.7 million to win a second term.

As of March 31, Ose had $501,000 on hand in his House campaign account. Boxer had $2.1 million in the bank.

Aside from the fundraising issue, ideology will also play a key role in Ose’s ability to challenge Boxer and, more importantly, to win a GOP primary. Several Republican observers predicted that if the moderate Ose emerged as the only top-tier GOP candidate he would likely draw one or more conservative primary challengers.

Ose isn’t the only House Member still pondering a Senate bid. Rep. George Radanovich (R) is also weighing a run and is likely to announce his decision within the next six weeks.

While Radanovich has also been discussing the election with potential donors and GOP officials, his entrance into the race is viewed as far less certain than Ose’s.

Elsewhere in the California Republican delegation, Rep. Darrell Issa has all but taken himself out of Senate consideration, instead choosing to focus on the effort to recall Gov. Gray Davis (D). Rep. Mary Bono (R) is also not expected to run.

Former Los Altos Hills mayor and U.S. Small Business Administration official Toni Casey (R) announced her candidacy on the Internet last week, while U.S. Treasurer Rosario Marin (R) is also considering a Senate bid.