United States Constitution
Article 1, Section 7
All bills for raising Revenue shall originate in the House of Representatives; but the Senate may propose or concur with Amendments as on other Bills.
The issuance of debt is a revenue raising measure. The "debt ceiling" is, in fact, legislation initiated in the House of Representatives, which authorizes the executive branch to issue debt through the treasury (and by extension the federal reserve), up to a specific limit.
This "debt ceiling" and authorization of debt issuance; allows the executive branch to raise revenue in a constitutionally legitimate way; because the revenue is raised under the auspices of specific authorization by the house or representatives.
Neither the Senate, nor the House, acting separately or together; has the authority or ability to delegate this exclusive power of the house, to any other entity, including the president. In fact, it would be a clear violation of the principle of separation of powers to do so.
That is all.