Read More Oil at $60, get ready for 'frack counterattack'
"It doesn't feel like it's quite over," said Emanuel. "But if you get better-than-expected (jobs data on Friday) that's the kind of thing that could cause more discomfort in the market and it might create a flush out of sorts, and that sets up the next buying opportunity."
ADP is expected to report at 8:15 a.m. ET that there were 205,000 private sector payrolls added in April, and while it's not necessarily a reflection of what's in the government report Friday, any jobs data is more important this month because of the surprisingly weak 126,000 March nonfarm payrolls.
Read MoreUS Treasurys extend losses after sell off
"If you have a very strong number, this market (Treasurys) could move to the downside," said Justin Lederer, rates analyst at Cantor Fitzgerald. Yields move opposite to bond prices. Lederer pointed to the drama in Treasurys where the 30-year yield rose above its 200-day moving average Tuesday, to 2.91 percent, and the 10-year traded above and then hovered near its 2.19 percent 200-day moving average.
"A lot of people are already looking toward Friday to see if last month was an outlier," Lederer said. Bond yields have risen faster at the long end, following the German bund which is responding to stronger data in Europe. With the launch of European quantitative easing, U.S. yields had moved lower in lockstep with the bund as the German 10-year got extremely close to zero and was expected to turn negative.
"It seems like whatever other markets are doing, the U.S. Treasury market is following. We're seeing some of the frothiness come out of the bund. To me it makes perfect sense for whatever reason, you could see some of the frothiness come out of U.S. Treasurys," said Jim Caron, global portfolio manager at Morgan Stanley Investment Management. Caron said he expects to see the bund yield continue higher.
Read More US economy probably shrank in Q1 after all: Moody's/CNBC survey
Economists Tuesday slashed their expectations for first-quarter GDP, which was reported last week at 0.2 percent. The consensus forecast for the second reading is now a decline of 0.4 percent, according tothe CNBC/Moody's Analytics Rapid Update. The jobs number will be the most important piece of second-quarter data so far, so it will be weighed carefully for what it may mean to the Fed in its move toward higher rates later this year.
Read MoreUS service sector growth rebounds in April: ISM survey
The timing of the Fed's first rate hike is now expected to be in September at the earliest, but every piece of data has the potential to create an outsize move in markets as traders try to handicap the timing.
The dollar traded lower Tuesday, with the euro falling back to $1.11, and its recent weakness has come in the face of higher yields.
In the stock market,the small cap Russell 2000 declined with the Nasdaq Tuesday, losing 1.4 percent, and the high-flying biotech IBB, iShares Nasdaq Biotechnology ETF lost 2 percent.
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