For either the fiance or spousal visa, you need to show that the two of you can support yourselves without needing to access public funds. The ECO processing your visa will be looking to see that you have at least £102.75 per week left over after paying rent and council tax (plus £57.57 per week for each independent child, if there are any).
In general the proof of income for the visa will come from the UK citizen as they are usually the one with a life and a job already set up in the UK and the US citizen will usually no longer have a source of income after leaving the US (i.e. they will be leaving their job to move to the UK). If you can meet this minimum requirement with her income alone, then any money you have will just be an added bonus.
