Senators voted Wednesday to make the first significant changes to the budget sequesters, shifting money to keep slaughterhouse inspectors on the job full time but refusing to rearrange money to reopen the White House for public tours.

The votes came as the Senate debated and passed a bill to fund the government through the rest of the fiscal year — sending it back to the House for final expected approval later this week and averting a government shutdown.

“This is indeed a very important moment,” said Sen. Barbara A. Mikulski, the Maryland Democrat and chairwoman of the Appropriations Committee who shepherded the bill through the floor. “We didn’t want brinkmanship, we didn’t want ultimatum politics.”

The 73-26 vote also signals a growing sense in Congress that the shutdown showdowns of the past two years didn’t help either party.

The bill funds basic operations through Sept. 30. It does not undo the level of sequester cuts, but it did begin to rewrite a few priorities, including restoring the military’s tuition assistance programs and restoring the money for food inspections.