When a RAII object fails to construct

Suppose I construct a RAII object, and that object may fail to construct. How do I handle this?

try {
    std::vector<int> v(LOTS);
    // try scope ends here because that's what the catch is for
} catch( const std::bad_alloc& ) {
    // ...
}
// v? what v?

Granted, the default constructor of std::vector won't throw and that can help, but this is not the general case. A constructor may very well throw. If I want to handle any resource acquisition failure, how do I do that while still being able to proceed if it doesn't throw?

Edit: To clarify, my issue is that if a resource fails to acquire then I might want to try again, and so on. Maybe I can try acquiring an alternative resource.