Republicans are pushing back plans to vote on a bill to make permanent the temporary provisions in the new tax law, CNBC has learned.

Rep. Rodney Davis, R-Ill., who introduced legislation to extend individual tax cuts, said he had hoped for a vote around Tax Day next week. Now the timeline is unclear, but he is speaking with leadership about bringing the bill to the floor.

A person briefed on the process, who spoke to CNBC on the condition of anonymity, said Republicans are worried about the optics of voting for potentially costly new tax cuts shortly after the Congressional Budget Office projected that the national debt will nearly equal the nation's entire economic output by 2028.