Had her language been accepted, it would not have been in order for the Senate to consider the budget plan that the Senate hopes to approve this weekend. The current unemployment rate sits at 7.7 percent, and the Democratic budget calls for $975 billion in new taxes over the next decade.

Ayotte's language did allow for a waiver, but that waiver would have to be approved by three-fifths of the Senate.

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"We should not be increasing taxes now at the expense of jobs," Ayotte said in the brief debate just before the vote.

"This budget asks the wealthiest Americans and our biggest corporations to pay just a little bit more, both to get our fiscal house in order, and to make critical investments that will help drive a broad-based economic growth," Senate Budget Committee Chairwoman Patty MurrayPatricia (Patty) Lynn MurraySenators press administration on mental health parity Top House, Senate Dems warn administration on short-term insurance Overnight Health Care: Opioid distributors summoned before Congress | Judge sets trial date in massive opioid lawsuit | Senators press DOJ to stop blocking medical marijuana MORE (D-Wash.) said in reply.

The two had the same fight over taxes in last week's Senate Budget Committee hearing, where Ayotte first called for language blocking consideration of any budget that raises taxes while unemployment is high.

Just before the vote on Ayotte's language, the Senate approved an amendment from Sen. Barbara MikulskiBarbara Ann MikulskiDems ponder gender politics of 2020 nominee Robert Mueller's forgotten surveillance crime spree Clinton: White House slow-walking Russia sanctions MORE (D-Md.) that would create a reserve fund allowing Congress to pass the Paycheck Fairness Act without adding to the deficit. That act boosts protection for women against salary discrimination.

Before the vote, Sen. John CornynJohn CornynTrump's NASA nominee advances after floor drama Senate GOP wary of new tax cut sequel Amid struggle for votes, GOP plows ahead with Cabinet picks MORE (R-Texas) said he encourages all senators to vote for this. Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsWu-Tang Clan jokingly enlists Comey to track down mystery album GOP lawmakers demand Sessions investigate Clinton, Comey Holder: 'Our democracy is under attack' MORE (R-Ala.) suggested a voice vote on this amendment, and the Senate approved it by voice.

After both votes, the Senate also approved a proposal from Murray to ensure tax relief for low- and middle-income Americans.

"The Senate budget already includes a deficit neutral reserve fund for tax relief," Murray said before the vote. "This amendment would make that relief for low and middle income Americans explicit, but it would do it in a way that preserves the healthcare benefits in the Affordable Healthcare Act."

Republicans said they do not oppose the language, but downplayed it by saying the Democratic budget raises billions in new taxes. The GOP said it would support a voice vote on the measure, but a roll call was taken and it passed 99-0.

Sen. Frank Lautenberg (D-N.J.) is not in this week, which is why many amendments will get 99 votes at the most.

— This story was updated at 12:04 p.m.