Sen. Scott said his amendment would raise awareness about a tax on premiums.
Only a small group in the House opposed the $200 billion legislation.
Senators backed year-round Pell grants for college students, but rejected a funding increase.
Senators rejected the measure in a 45-55 vote.
The paid sick days amendment was offered by Sen. Patty Murray (D-Wash.).
"America does not project power from bankruptcy court," he said.
The amendment would have raised spending above the mandated budget caps.
Sen. Debbie Stabenow said her amendment was designed to bring jobs back to America.
Schock delivered his farewell and also broke House rules, posing for a floor pic.
The amendment would have created a budget placeholder for a wage increase.