To ensure correct cross-browser behaviour, I think you should parse the string yourself. I moulded this answer into:
function msFromString(dateAsString)
{
var parts = dateAsString.match(/(d{4})-(d{2})-(d{2}) (d{2}):(d{2}):(d{2}).(d{3})/);
return new Date(parts[1],
parts[2] - 1,
parts[3],
parts[4],
parts[5],
parts[6],
parts[7]).getTime();
}
console.log(msFromString("2011-05-12 16:50:44.055"));
This outputs 1305211844055
.
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