From the policy statement, the FOMC made it clear it's much more concerned about the slowing economy than inflation. The vote for the rate cut was unanimous. Even the committee member Richard Fisher who has been an inflation hawk, voted for this policy action.
Economists quoted in the CNN article are mixed on whether we'll see cuts below 1%. One said that the unanimous vote signals that they're not done in lowering rates especially if the economy continues to weaken. Other economists see the rate cut as useless in helping the economy since banks are unwilling to lend.
Competition among banks has kept interest rates up this year as described by this BestCashCow article. Hopefully, this will keep pressure on the banks to keep rates from falling. But with the funds rate at only 1% and with continued economic weakness, I'm afraid we should expect some declines in savings account and CD rates.