The move marks a departure from House leadership as Capito prepares for a Senate run in 2014.
Capito goes on to say that West Virginia has suffered three major natural disasters over the past year, which have "placed a significant burden on the State ... and its localities, making it important that supplemental funding be made available to help communities recover from the effects of Hurricane Sandy." A portion of the funding in the extended aid package is slated for use outside of the New York/New Jersey-area epicenter of storm damage.
"While all of us understand the need to be fiscally responsible in this era of record federal deficits, our country has always come together as one to provide assistance to communities who suffer from a major natural disaster," she concludes in the letter, calling for passage of the legislation.
Capito joined a majority of her fellow House Republicans in voting against a bill to avoid the "fiscal cliff" of tax increases and budget cuts late Tuesday night.
The measure, however, passed the House 257-167. Following that vote, the House adjourned for the night and Boehner declined to bring the Sandy aid measure up for a vote.
The Senate has passed a $60 billion measure to provide supplemental disaster relief, but Republicans say the bill funds projects not related to the storm-recovery effort.
New Jersey and New York lawmakers from both parties blasted Boehner's decision not to take up the bill in speeches on the House floor, with New York GOP Rep. Pete King suggesting in a Thursday vote that he might not support Boehner for Speaker.
King also suggested in a Wednesday interview on Fox that people in the Northeast should not donate to congressional Republicans because of the Sandy issue.
And donations might be on Capito's mind, as she recently announced her intention to run for Sen. Jay Rockefeller's (D-W.Va.) seat in 2014.
Capito might also hope to burnish her centrist credentials in advance of a run in a state that voted for Republican presidential contender Mitt Romney and reelected Democrat Joe Manchin to the Senate in 2012.
Rockefeller has won in each of his five elections with more than 50 percent of the vote, and remains a strong contender if he chooses to run again in 2014, though he is considered a top retirement risk for Democrats.
Although West Virginia has grown increasingly red in recent years, Capito will need to win centrists to take the seat, and coming out against Boehner's Sandy stance could help her make her case to those voters.