Sen. Marco Rubio and others are disappointed in the numbers in the Senate budget.
Sen. Jon Tester's bill eases the VA's "burden of proof" standards.
The so-called "doc fix" passed the House on Thursday.
The Republican budget resolution was approved early Friday morning in a 52-46 vote.
The amendment cuts the employer contribution to health coverage for lawmakers.
Eleven Republicans voted for the amendment.
Sen. John Thune (R-S.D.) said "a death in the family should not be a taxable event."
Senators have been voting since noon Thursday as part of the budget amendment process.
Sen. Ed Markey said the amendment undercuts President Obama's authority.
The amendment would have blocked $1.2 trillion in Medicaid cuts.