The Senate on Tuesday advanced a key part of President Obama's embattled multi-national trade agenda by voting to end debate on fast-track authority.

The 60-37 vote overcame a supermajority threshold and paves the way for a series of votes this week. Lawmakers hope to send the group of trade bills to Obama before the July 4 recess starts next week, according to USA Today.

Thirteen of the chamber's 44 Democrats voted for the legislation, and were joined by 47 of the Senate's 54 Republicans, according to Reuters. The bill needs 51 votes to pass.

Fast-track, otherwise known as trade promotion authority (TPA), would give the president the authority to send his three trade agreements through Congress without allowing for amendments - only an up or down vote on the final deal.

Receiving fast-track authority is critical to Obama being able to complete the 12-nation Trans-Pacific Partnership (TPP), which he says would strengthen U.S. ties with Asia.

Along with the TPP, the other two accords being finalized are the Transatlantic Trade and Investment Partnership (TTIP) and the Trade in Services Agreement (TiSA).

TPA already passed the Senate last month, in a legislative package that included TAA, which provides help to American workers who lose their jobs due to trade deals.

But House Democrats rebelled against Obama and rejected TAA, which many on the left support, in an effort to slow down TPA and in turn, the TPP.

In a rare alliance, Republican leaders and the White House formed a new strategy that would first pass fast-track and then TAA separately.

If TPA makes it through Wednesday's vote, lawmakers will likely vote on TAA on Thursday, according to The Hill.

While Senate Majority Leader Mitch McConnell, R-Ky., praised Tuesday's passage as "an important moment for the country," opponents, like Sen. Bernie Sanders, I-Vt., said it's against the best interests of the majority of Americans.

"This agreement was opposed by every union in this country, working for the best interests of working families by almost every environmental group and many religious groups," said Sanders, a candidate for the 2016 Democratic presidential nomination, according to USA Today. "It's a great day for the big money interests, it is not a great day for working families."