Tax Cuts and Jobs Middle Class Enhancement Act This bill amends the Internal Revenue Code to exclude from gross income up to $5,000 received by an individual as a bonus after December 22, 2017, and before January 1, 2019. The bill defines a "bonus" as amounts paid to an employee other than amounts obligated under an employment contract. The bill makes permanent the tax reductions and other provisions for individuals that were enacted in P.L 115-97 (commonly known as the Tax Cuts and Jobs Act) and are scheduled to expire at the end of 2025. The bill also: increases the standard deduction, makes permanent the reduction in the adjusted gross income threshold that must be exceeded before a taxpayer is allowed to claim an itemized deduction for medical expenses, and increases the refundable portion of the child tax credit.