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The Vermont senator, who is mulling a 2016 White House bid, said there has not been "a lot of transparency" on the Trans-Pacific Partnership (TPP) legislation.

"Not only is there massive opposition to this TPP agreement, but there is a lot of concern that the American people have not been involved in the process, and there's not a lot of transparency," Sanders said.

The Finance Committee is expected to take up trade legislation Wednesday afternoon to give President Obama fast-track authority to push new trade deals through Congress with up-or-down votes.

McConnell said that because of Sanders's objection, the Finance Committee will still meet, but the Senate will have to recess.

"All this objection is going to do will be to require us to recess after the votes on trafficking and stay in session, because we're going to finish the bill in the Finance Committee today," McConnell said. "I'm just making the point that this particular way to oppose it will not be successful today."

The Kentucky Republican added the "committee will simply be inconvenienced by the current actions of the senator from Vermont."