By Ben Eisen, MarketWatch

NEW YORK (MarketWatch) -- Treasury prices mostly fell Tuesday, sending yields higher, as the market begins to anticipate a spring rebound in economic data, following an unusually cold winter that helped push benchmark government debt prices to their best quarter since June 2012.

The 10-year note (10_YEAR) yield, which rises as prices fall, was up 3.5 basis points on the day to 2.761%, according to Tradeweb. The 30-year bond (30_YEAR) yield rose 4 basis points to 3.603%, while the 5-year note (5_YEAR) yield rose a basis point to 1.741%.

In the quarter ended Monday, the benchmark 10-year yield fell over 25 basis points, the biggest drop since the quarter ending in June 2012, as the bond market defied expectations that yields would rise in 2014, according to FactSet. The Barclays U.S. Aggregate bond index, which measures the performance of a broad basket of bonds, returned 1.8% last quarter, while the S&P 500 index (SPX) only returned 1.3%.

While data is expected to rebound in the spring thaw, Treasury prices mostly dropped on Tuesday for technical reasons.

"People were buying over month-end for index extension. After that, they are reevaluating their portfolios," said Ira Jersey, interest-rate strategist with Credit Suisse Group AG. He added that since then asset managers and mutual funds have been getting short the market.

The premium that longer-term yields pay over short-term yields rose Tuesday, in a reverse of recent trading patterns that had seen intermediate sector yields, known as the belly of the curve, sell off. "This is the first time in a while we haven't seen the belly leading," Jersey said.

That so-called steepening of the yield curve came after Federal Reserve Chairwoman Janet Yellen gave a speech Monday that calmed markets about increases to the central bank's target policy rate. But the narrowing and widening of the differential between shorter- and longer-term yield may continue.

"These are the things that end up being a part of the market when you are worried about rate increases," said Tom Tucci, managing director and head of Treasury trading at CIBC World Markets Corp.

Data on Tuesday provided a slight dose of optimism that economic activity would rebound. The Institute for Supply Management said Tuesday that manufacturing companies expanded slightly faster in March, with its index rising to 53.7% from 53.2%. A reading over 50 indicates growth.

The final U.S. Markit purchasing managers index came in at 55.5 in March, down from 57.1 in February. Construction spending in February notched up 0.1%. Chrysler reported 13% sales growth in March while Ford Motor Company (F) sold 3% more units.

The market is looking forward to a nonfarm payrolls report on Friday. Economists expect 200,000 jobs have been added in March, up from 175,000 in February.

Strategists at Credit Suisse wrote in a Tuesday report: "The market will focus on employment-related data this week, with the consensus converging on a continued rebound from the early year weakness. A strong print on Friday could be the first step towards improving spring data leading to a more sustained sell-off."

But given high expectations that have pushed the market's "whisper number" for new jobs created above 200,000, the market may be primed for a disappointment, said Tucci, of CIBC.

Treasury prices began falling Tuesday after slightly optimistic data on Chinese and euro-zone manufacturing. China's official manufacturing gauge rose to 50.3 in March from 50.2 in February. Euro-zone's March PMI hit 53.0 in March. While that number is down from 53.2 in February, a reading above 50 indicates month-to-month growth.

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