Actually, Chris Lercher hit the nail on the head, but he only made it in a short comment, so I wanted to expand on it.
Imagine two stopwatches; one is somewhere where UTC is the local time on Jan 1, 1970, and the other stopwatch is local to your area (let's say that it's in New York, 5 hours after UTC). At UTC midnight, on Jan 1, 1970, the UTC stopwatch is started. 5 hours later, your local stopwatch is started. Those two stopwatch times differ by some amount, determined only by what the difference between UTC was from your local time at local midnight on Jan 1, 1970. Any daylight-saving shenanigans, since then, have no bearing on the difference between those stopwatches. So, any DST corrections for your present time or for the times you're converting, are irrelevant. All you need is how much later your local stopwatch started on Jan 1, 1970.
As Chris pointed out, this is just: getOffset(0L), so:
int offset = TimeZone.getDefault().getOffset(0L);
long newTime = oldTime - offset;
... should work fine. However....
To help really grasp this, note this: that "0L" in getOffset() is the milliseconds since the UTC epoch (which is the only real epoch). So, your offset variable is going to have the number of seconds of offset at midnight UTC (ie, when it was, say, 19:00 on 12/31/1969 in New York). If your local time switched to/from daylight-saving in those last hours before local midnight, then getOffset(0L) wouldn't be correct. You need to know what your daylight-saving status was at local midnight, not UTC's midnight.
I'd be surprised if this were the case, anywhere (ie, any timezone which changed to/from DST between their local midnight and UTC midnight of Jan 1, 1970). However, just for fun, a cheap hack to help guard against this would be to check if the offset changed in those hours:
// Offset at UTC midnight
int offset = TimeZone.getDefault().getOffset(0L);
long newTime = oldTime - offset;
// Offset at Local midnight
int localMidnightOffset = TimeZone.getDefault().getOffset(-offset);
Here, localMidnightOffset will be what the timezone offset was at a time -offset milliseconds after UTC midnight in 1970. If no DST change happened, then localMidnightOffset will equal offset, and you're done. If some DST change did occur, then you might have to hunt around... probably keep doing a
localMidnightOffset = TimeZone.getDefault().getOffset(-localMidnightOffset)
until it stops changing... and hope you don't get caught in an endless loop. I'm curious to see if anybody has a guaranteed-converging solution.
Kinda makes you wish the world were flat, huh?