Get new bits (1/8"). When the bit starts to dull the hole will be slightly undersized and the rivet will be tight. High speed steel should be fine you are only drilling aluminum and it shouldn't take much to get through them.
1/8 inch drill bits are not for 1/8 inch pop rivets. It is near impossible to drill a perfectly round hole with a hand held drill.
Using a 30,000 rpm hand held drill with a new 1/8 inch drill bit, will still not give you a perfect "round" hole.
To repair any Airstream, use the following drill bits.
For 1/8 inch pop rivets use a #30 drill bit.
For 5/32 inch pop rivets or Olympic rivets use a #21 drill bit.
For 3/16 pop rivets use a #11 drill bit.
Hardware stores usually do not carry numbered drill bits, but Home Depot and the like do.
Some hardware stores will think your senior moments are on an extended tour of duty if you ask them for a numbered drill bit. But then, if you asked them for a letter drill bit, they will know you lost it all together.
Seriously, there are no exceptions to the drill bit sizes, when you are repairing any Airstream product.
Wallowing out holes to make the pop rivets fit, is crude at best.
Not to re-ignite the great drill bit debate but I did find a #30 drill bit on Yahoo Shopping. I did call a local tool supply company and they have the #30 on order.
This one looks more like a traditional bit. The #29 I saw at Lowe's looked like it had screw threading on the sides.
I just replaced 1/2 of my rub rail. I used 2 BOSCH Titanium bits that both broke. I bought two more but also bought a Dewalt 1/8" bit. The Dewalt (Cobalt) works really well.
FYI - The only second rate work was the work done by the factory! Those holes underneath looked like interns or new-hires installed my rub rail!
Also, I used the 1/8" diameter "LONG" (1/2" length?) aluminum pop rivets from Lowe's. (Thanks Brett!)