So far, so good for Sen. Lisa Murkowski’s uphill write-in bid for re-election, according to a new CNN/Time poll. Joe Miller (R) takes 38 percent, Murkowski has 36 percent and Scott McAdams has 22 percent, among the 927 likely voters polled.

Murkowski is trying, against the odds, to win November’s general election after losing the August GOP primary.

Her share of supporters in the survey includes “nearly four in 10” Democrats, according to CNN Polling Director Keating Holland, who called that “an indication that a lot of Democrats are more interested in defeating Miller than they are in electing a member of their own party.”

The poll was conducted Sept. 24-28 and had a 3-point margin of error.