The battle over the American Jobs Act has sucked up all the oxygen, but there’s another jobs fight you really should be keeping an eye on: The battle over the measure to punish China for currency ma­nipu­la­tion.

It’s a really interesting story, and it’s going to heat up in a big way next week. A lot is riding on the outcome — according to one estimate it could create over 1 million jobs. House Dem leaders like Nancy Pelosi are pushing hard for it, and passage could help shore up vulnerable Democratic Senators in swing states that have hemorraged manufacturing jobs to China.

It’s also creating an interesting tension with the White House, which seems to be cool to the idea, partly for reasons involving diplomacy and trade. This could put Obama at odds with Congressional Democrats, as well as liberal bloggers and unions, over a key jobs creation measure — one that has considerable populist appeal amid public anger over unemployment — just at a moment when Obama is striking a more populist tone heading into 2012.

Earlier this week, Harry Reid announced that he would hold a vote next week on the bill — which would slap tariffs on China for allegedly depressing the value of the yuan to keep wages low — before holding one on Obama’s jobs measure. The China bill has growing bipartisan support — Republicans whose states have suffered outsourcing like it — so it’s expected to pass the Senate.

But the measure remains bottled up in the GOP-controlled House. Democratic leaders have been circulating what’s known as a “discharge petition” to force a vote on the measure, and according to Democratic aides, it now has 174 signatures — bringing it close to the 218 it needs to force the vote.

The rub: Not a single House Republican has signed the petition to bring the measure to the floor. This, despite the fact that the bill passed the House with overwhelming bipartisan support in 2010, with 99 Republicans supporting it (there was no vote in the Senate on it). And Dems are demanding to know why.

“Last year, Republicans joined Democrats in passing this bill and it has strong support today,” Pelosi spokesman Nadeam Elshami tells me. “Republican leaders who continue to stand in the way must explain to American workers why they must pay the price for inaction in the House.”

Asked why no Republicans have signed the discharge petition despite previous support, a House GOP leadership aide would only say: “I suspect we share the White House’s concerns.”

The White House’s position remains unclear. Yesterday spokesman Jay Carney declined to say whether Obama would support the Senate bill, though he said: “we share the goal of achieving further appreciation of China’s currency.”

This reluctance has angered some Dems. Senator Sherrod Brown, a leading proponent, argues that if Obama fails to support the bill, “it’ll be harder everywhere for him,” adding: “Ninety percent of the American public thinks we need to do more manufacturing in this country.” Still, Dem aides expect Obama to sign the bill — if they can get it through Congress. The next steps: The Senate bill next week, and more pressure on House GOPers via the discharge petition.

Keep an eye on this one.