Our HOA botched assessment for replacement project. Do over?

I am the president of my HOA in California. We recently passed a special assessment to replace the siding on all our buildings. The assessment was passed by majority vote (as required by our by-laws). The assessment amount was based on a ballpark estimate from one of our contractors. Once the assessment was passed, we quickly learned that the assessment amount was too low to cover the costs for a complete siding replacement. All the bids came in much higher.

Rather than scrapping the assessment and doing another vote for a higher assessment amount (which we don't think will pass due to the tough economic conditions), the HOA Board would like to use the approved assessment amount to replace the siding on the back of the buildings only (which is in worse condition than the front). We would like to know if this is legally permissible. The original intent of the assessment was to replace all the siding, not just partial.