The available evidence shows that some undocumented immigrants contribute federal taxes, but it does not establish that more than half of the entire undocumented immigrant population does so. The claim also leaves “federal taxes” and “pay” undefined, which could refer to different taxes and measures.
Most undocumented immigrants in the United States pay federal taxes.

Undocumented Immigrants Fear Tax Data Will Be Shared With ICE - The New York Times
Source: nytimes.com
Key Evidence
The approved sources provide evidence about aggregate tax contributions and related groups, not a direct percentage of all undocumented immigrants who pay a specified federal tax.
Evidence involving ITIN filers does not resolve the claim because it may include non-undocumented people or use a household denominator rather than the full undocumented immigrant population.
The sources do not use one consistent definition of “federal taxes” or “pay,” leaving unresolved whether the relevant measure is income, payroll, excise, or indirect taxation.
What the Evidence Shows
The central proposition is a current majority claim: more than half of all undocumented immigrants in the United States must be shown to pay federal taxes under a defined measurement. The approved evidence does not provide that population-wide percentage.
The cited material addresses related but different measures, including aggregate tax amounts, workers, households, individual tax-identification-number filers, and mixed populations. Those measures can show that undocumented immigrants contribute some federal taxes, but they do not establish the share of the full undocumented immigrant population that pays them. In particular, an aggregate total cannot be converted into a percentage of people without a matching denominator, and an ITIN-filer figure may include people who are not undocumented or use a household rather than individual denominator.
The wording “federal taxes” is also materially ambiguous. Payroll withholding, federal income-tax filing or payment, excise taxes, and indirect contributions could produce different payer shares. The approved sources do not supply a current, consistently measured result covering the full population under one specified definition. The available evidence consequently cannot determine whether the claimed majority exists.