Senators reached a deal Wednesday to move forward on President Obama's trade agenda only one day after Democrats embarrassed him by blocking it. 

Lawmakers said roughly a dozen Senate Democrats agreed to let full-blown debate begin after both parties' leaders consented to tweak the package that failed on a procedural vote Tuesday. Those Democrats' votes were the difference between blocking the agenda and letting it move ahead. 

The breakthrough doesn't assure Obama of receiving "fast track" negotiating authority, which would let him send to Congress trade proposals it can kill or ratify, but not amend. That's still subject to weeks or months of Senate and House debates, amendments and votes. 

But the breakthrough gave the White House a welcomed respite from the negative headlines stemming from Tuesday's setback, which was driven entirely by Democrats. 

Most Democratic lawmakers oppose free-trade agreements, saying they reduce U.S. jobs. Labor unions and liberal groups, which are vital to Democrats' campaigns, strongly oppose fast track. 

Tuesday's impasse involved side issues including a proposal to punish countries that keep their currency artificially low to boost exports. Wednesday's agreement calls for a stand-alone vote on "currency manipulation" sanctions, possibly as early as Thursday. 

A vote on fast track would come later, possibly next week.