But this is not Ms. Raimondo’s only problem: Mr. Fung has $272,000, to Ms. Raimondo’s $33,000.

She started behind because she opted out of a matching-funds program, which allowed her to spend whatever she wanted on the primary; she spent more than $5 million. Mr. Fung, who accepted the matching funds, received $1.1 million for the general election. The Democratic Governors Association has bolstered her television presence with $755,000. Mr. Fung has received $125,000 from the Republican Governors Association.

But she faces other challenges. Rhode Island has never elected a female governor, and she created a stir when she said she would seek to repeal a 1997 law banning partial-birth abortions.

Apart from being heavily unionized, Rhode Island is heavily Roman Catholic, and her stance landed Ms. Raimondo, who is Catholic, in hot water with the church. Bishop Thomas J. Tobin of the Providence Diocese said she had taken the “extreme” position for political gain, and La Salle Academy, the Catholic school in Providence from which she graduated in 1989 as valedictorian, removed her picture from its wall of notable alumni.

She subsequently said she would support the ban if it included exceptions to preserve the health and life of the woman. (Despite calling himself “pro-choice,” Mr. Fung, who opposes partial-birth abortions and taxpayer funding for abortions, has received the endorsement of Rhode Island Right to Life.)