“This nasty and backwards budget green-lights cuts to Medicare and Medicaid in order to give a tax break to big corporations and the wealthiest Americans,” Mr. Schumer said.

The Senate approved the budget blueprint after considering a flurry of amendments, a tedious process that gives the minority party an opportunity to force the majority to endure politically difficult votes. One Democratic amendment that was rejected sought to stop tax cuts from going to the top 1 percent; another would have restored cuts to Medicare.

The Senate approved the budget after a so-called vote-a-rama, a legislative whirlwind in which amendments are considered one after another. One proposal would have deleted language that could allow for drilling legislation; the amendment failed, 48 to 52.

“The Arctic National Wildlife Refuge is one of the most pristine areas of the United States, and we have been protecting it for decades for a reason,” said Senator Maria Cantwell of Washington, the top Democrat on the Energy and Natural Resources Committee.

But Senator Lisa Murkowski, Republican of Alaska and the chairwoman of the energy panel, said erasing the language would “deprive us of a substantial opportunity to benefit our country at the same time that we care for our environment.”

In Congress, the annual budget resolution provides an outline of federal spending and revenues. The Senate’s blueprint, for the 2018 fiscal year that began Oct. 1, claims to achieve a balanced budget within a decade, assuming greater economic growth and using an accounting method that excludes Social Security. In order to erase projected deficits, it calls for trillions of dollars in spending cuts over the coming decade.