WASHINGTON (AFP) - Things are not quite square in Washington when the biggest backer of President Barack Obama's current legislative priority is the Senate's top Republican and its arch foe is the Democratic leader.

Yet that is the scenario in the United States Senate, which holds a test vote Tuesday on whether to consider giving Obama fast-track trade promotion authority (TPA) to complete a massive trade deal with 11 other Pacific rim countries.

Senate Republicans mostly support the measure, which would allow Obama to present a trade deal to Congress for an up or down vote, but with lawmakers forfeiting rights to make changes.

Several members of Obama's Democratic Party are highly critical of TPA because it would let the president ram through a pact that they argue would siphon American jobs to places like Vietnam and fails to include enforceable language on preventing currency manipulation.

As a result, Obama has been doing his most serious political arm-twisting since the Affordable Care Act of 2010, lobbying dozens of skeptical lawmakers.

"The president has been in frequent conversations with members of Congress, mostly Democrats, but some Republicans," White House spokesman Josh Earnest said.

Senate Democratic Minority Leader Harry Reid, who is against the Trans-Pacific Partnership (TPP), said he opposes debating TPA until the Senate addresses more pressing issues, such as the June 1 expiration of bulk-data collection authority by the National Security Agency.

As for the trade deal, while it is being negotiated in secret, Reid said the White House has kept him at least somewhat informed.

"I know how bad it is," Reid sneered.

Such is Reid's command over Senate Democrats that many of them are expected to back his delay tactics.

"It's going to be a very close vote," a senior Democratic aide said.

Senate Republicans would need at least six Democrats, but perhaps twice that, to reach the required 60 votes in the 100-member chamber.

Last week, Senate Majority Leader Mitch McConnell, perhaps not wanting to appear too comfortable working hand in glove with Obama, described his close TPA work with the White House as "almost an out-of-body experience." He warned Monday that it would be a "big mistake" to block TPA, but sounded less than certain about its success.

Asked by AFP whether he felt the measure had enough votes, McConnell said "we'll find out tomorrow, won't we?"

'Just don't do it'

Securing passage in the House of Representatives, also led by Republicans, is likely to prove even more difficult.

Some 60 Republicans, most of them aligned with the ultra-conservative Tea Party movement that is reluctant to provide Obama with a major victory, are reportedly expected to balk at voting for TPA, despite a full-court press by popular GOP figures like Ways and Means Committee Chairman Paul Ryan.

That would mean the support of dozens of Democrats would be needed.

Committee spokesman Brendan Buck said leadership was holding "listening sessions" and other outreach to bring skeptics on board.

"We remain confident we will provide a strong number, but, as always, will need Democrats to deliver as well," Buck said.

In a late TPA push, Obama traveled last week to Nike's Oregon headquarters to highlight how the shoe giant could create 10,000 new jobs if the Asia-Pacific trade pact comes into being.

"Just do it," Obama said, repeating the company's trademark slogan.

But critics, including some of Obama's closest supporters on most other issues, lashed out at the deal as bad for American workers.

"If it passes, TPP will encourage Nike's exploitative business model in the largest trade agreement in history," tweeted House Democrat Rosa DeLauro, using the hashtag #JustDontDoIt.

Liberal Senator Elizabeth Warren warned that TPA could roll back rules governing Wall Street banks after the 2008 financial crisis.

Obama rejected Warren's claims, telling Yahoo News that his longtime ally's "arguments don't stand the test of fact and scrutiny."