According to the USCIS, as of June 1, 2012, the agency had received 55,600 out of 65,000 available cap-subject H-1B petitions for FY-2013 and 18,700 out of 20,000 available petitions under the H-1B Masters Cap Exemption.
The pace of filings accelerates as the cap gets closer to being exhausted. It is likely too late to begin working on a cap-subject H-1B petition today. Given that it takes seven days for the LCA to be certified, by the time the petition is actually filed with the USCIS, the cap will, in all likelihood, have been exhausted. Those that are in works and ready to be filed in the ext few days stand a good chance of getting one of the few remaining receipt numbers.
Remember that this limitation applies only to H-1B cap-subject cases. Some organizations are cap exempt. Finally, if an H-1B is not available, perhaps you are eligible for another status. A consultation with a qualified immigration attorney may help you come up with an immigration strategy that suits your specific needs.