First, I'm assuming you're speaking of RSA 1024 bit encryption.
Generally, the topic is far too complicated for providing a simple number.
tl;dr: Cracking an OpenPGP encrypted message on a single CPU is not feasible, and probably takes years even with large computing clusters. Yet unknown (to the public) mathematical flaws could change this by order of magnitude, as quantum computers might do at some time in future (far, from an "internet age" point of view).
The slightly longer version:
Cracking the Asymmetric Encryption (RSA 1024 bit key)
In addition to RSA 1024 bit keys, this also applies to larger key sizes. Larger keys provide more security (in form of computing power to crack them), but remember the security does not increase linearly with the key size.
There's a nice post on the Information Security Stack Exchange, "How to estimate the time needed to crack RSA encryption?", which does not complete with an estimate like "Using an Core i7 model xy, you'll be able to crack an RSA 1024 bit key in estimated z hours", but the answers agree on "RSA 1024 bit keys cannot be cracked by individuals with usually available computing power (ie., a handful of high-end machines) in a reasonable time.
The discussion of breaking 1024 bit keys with much more computation power was only considered from an academic point of view:
I recently learned that the selection of the parameters for a 1024-bit number factorization has begun (that's the "brainy" part); the sieving is technically feasible (it will be expensive and involve years of computation time on many university clusters) but, for the moment, nobody knows how to do the linear reduction part for a 1024-bit integer. So do not expect a 1024-bit break any time soon.
This probably also applies to large, well-funded institutions with lots of computing power like the NSA.
Things could change rapidly if
- somebody finds a mathematical flaw, which reduces RSA's complexity by orders of magnitude (some institutions like the NSA employ a vast number of great mathematicians), or
- quantum computers finally work and get powerful enough and capable of running certain algorithms. Not expected to occur within the next few years.
For DSA/ElGamal, things are a little bit different. A DSA key of the same size of an RSA key provides more security, but at the same time DSA is more vulnerable to bad random numbers (compare with the Debian random number generator flaw). Elliptic curve cryptography which is upcoming for OpenPGP right now does not have known attacks for the algorithms supported yet and generally considered safe, but there is some doubt left especially on the NIST-recommended curves (NIST has lost quite some reputation for making a broken random number generator a standard), and some implementation nitpicks.
Cracking the Symmetric Encryption
For performance rasons, OpenPGP uses hybrid encryption, thus the message gets encrypted with symmetric encryption and a random symmetric key (in OpenPGP, often called "session key"). This session key again is encrypted using the asymmetric encryption algorithm, eg. RSA.
If you're able to crack the symmetric encryption key of a message, you could also read the message (unlike cracking the asymmetric key, where you could read all messages encrypted to this key).
Unlike with very early versions of PGP (which used a symmetric encryption algorithm designed by Zimmermann himself called BassOmatic, which is considered broken), all symmetric algorithms defined for OpenPGP do not have relevant known attacks.
Unless somebody chose to use no symmetric encryption (which is actually possible!), breaking a message using the symmetric encryption algorithm should not be considered feasible at the time being.