The party who owes 2000 yuan on his credit card and fails to repay it according to the agreement and relevant laws for a long time is a breach of contract and needs to bear the corresponding liability for breach of contract according to law. Please verify and determine the specific situation according to the actual situation and relevant laws and regulations.

Relevant legal provisions: People's Republic of China (PRC) Contract Law.

Article 107 If a party fails to perform its contractual obligations or fails to perform the contractual obligations in conformity with the contract, it shall be liable for breach of contract such as continuing to perform, taking remedial measures or compensating for losses.

Article 108 If a party expressly expresses or shows by his own behavior that he will not perform his contractual obligations, the other party may require him to bear the liability for breach of contract before the expiration of the performance period.