At the core of Republicans’ sprawling domestic policy package is an important political calculation. It provides its most generous tax breaks early on and reserves some of its most painful benefit cuts until after the 2026 midterm elections.

The result is a bill that, if it becomes law, may generate bigger refunds for some taxpayers when they file their returns next spring, even as a series of significant changes to Medicaid and other aid programs loom as a future threat to the finances of poorer families.

For President Trump, the staggered timelines underscore the political risks in his signature legislation, which passed the Senate on Tuesday and now awaits a final vote in the House. To pay for the tax policies, which confer their greatest benefits on the wealthy, Republican lawmakers have looked to slash programs that are both popular and widely used, discomfiting even some within their own ranks.

The savings from the safety net cuts still are not enough to offset an expensive package of tax breaks that is projected to add more than $3 trillion to the federal debt by 2034.

Some of the proposals, including those that could see millions of people lose Medicaid and food stamps, are unlikely to be viewed favorably by voters. That reality led some Senate Republicans to oppose the domestic policy bill this week, citing the potential adverse impacts on their states and residents.

Matthew D. Dickerson, the director of budget policy for the Economic Policy Innovation Center, a conservative group, said the timeline reflected a lesson that Republicans had learned in Mr. Trump’s first term, when they passed a package of tax cuts in 2017.