Rep. Colleen Hanabusa (D-Hawaii), who is considering running in a 2014 primary against either Hawaii Gov. Neil Abercrombie (D) or the man he appointed to the Senate, Brian Schatz, met with officials at the Democratic Senatorial Campaign Committee on Thursday, according to three people with knowledge of the meeting.

From left, U.S. Rep. Colleen Hanabusa, U.S. Rep. Mazie Hirono, U.S. Sen. Daniel Inouye, Hawaii Gov. Neil Abercrombie and candidate Tulsi Gabbard celebrate their election victories at the Japanese Cultural Center, Tuesday, Nov. 6, 2012 in Honolulu. (Marco Garcia/AP)

Three people familiar with Hanabusa's thinking said it's very likely she'll run for one of the two statewide offices (and not reelection), but said she hasn't made up her mind about which one.

"She’s struggling mightily between governor and Senate and has not made up her mind yet, but should do so shortly," said one person close to Hanabusa, who was granted anonymity to speak candidly about her plans. "Chances are pretty good that she won’t stay in her current job."

Hanabusa emerged as the favorite to win an appointment to the Senate following the December death of her close political ally, longtime senator Daniel Inouye (D-Hawaii), and Inouye made clear he wanted her picked for his seat.

But Abercrombie surprised many by instead picking his then-lieutenant governor, Schatz, and touched off a controversy in the process.

Hanabusa has reportedly seen some favorable polling in both the governor's race and the Senate race which, as many Democratic primaries in Hawaii do, would pit a Caucasian candidate against an Asian-American one.

While Schatz remains somewhat unknown following his appointment, Abercrombie has struggled with a poor approval rating that has made him susceptible to a primary challenge.

Either race would seem to be potentially fertile ground for Hanabusa.

If she were to run for Senate, it could cause headaches for the national party -- forcing the DSCC to decide whether to back the appointed Schatz and potentially pitting it against the women's group Emily's List -- but likely wouldn't endanger the seat in the country's bluest state. Hawaii went 71 percent for President Obama last year and also gave then-Rep. Mazie Hirono (D) a comfortable 25-point win over former two-term governor Linda Lingle (R) in the race for the state's other Senate seat.

The DSCC hasn't said whether it would back Schatz in the still-hypothetical primary, but DSCC Chairman Michael Bennet (D-Colo.) and Senate Majority Leader Harry Reid (D-Nev.) have both contributed to Schatz's campaign.

There is some precedent for a sitting senator facing a primary challenge in Hawaii. In 2006, then-Rep. Ed Case launched an ill-fated primary campaign against Sen. Daniel Akaka (D-Hawaii).

More recently, in 2010, Bennet (who is also an appointee) narrowly beat back a tough primary challenge from former Colorado state House speaker Andrew Romanoff.