The target increase came as a "true sense" of the scale of flood damage became clear, a spokesperson said.
Andy Beeforth, chief executive of Cumbria Community Foundation that launched the appeal, said the floods had "impacted more severely" than previous floods.
Meanwhile, the farming minister said funding for farmers was a "priority".
The delayed money for farmers affected by the floods was due to be handed over by the Rural Payments Agency in the new year following a computer error, but may now be received earlier, the minister said.
More than £166,000 has been handed out in grants and families have been given financial help to rebuild their lives, the foundation said.
The appeal was launched 12 days ago on 5 December after a record level of rainfall devastated parts of Cumbria.
Ian Brown, chairman of the foundation, said he was "overwhelmed" by the generosity of people donating to the appeal.
"People see the photos, see the need for help and are creating fundraising events and digging deep into their own pockets.
"It's very heart-warming, very encouraging to see," he said.
The target for the Cumbria Flood Recovery Appeal has increased to £5m after raising £2m since Storm Desmond.