"Reflecting the upward revisions to retail sales, and faster-than-expected construction spending and business inventories, we boosted our Q1 GDP tracking estimate by four tenths to 1.2 percent," wrote Goldman Sachs economists.

The CNBC/Moody's Analytics Rapid GDP update median tracking forecast is now 1.5 percent, up 0.2 percentage points from last week. Economists also put second quarter growth at 2.7 percent.

First quarter growth forecasts are now tracking solidly between 1 percent and 2 percent, following a recession scare that had some economists' forecasting growth barely above zero.

J.P. Morgan economists were even more optimistic. "We now believe real annualized GDP growth last quarter is tracking 2.0 percent, up from our prior estimate of 1.5 percent," they wrote. "Much of that upward revision is coming from stronger inventory accumulation, which may add some downside risk to our projection of 2.25 percent growth in Q2."

The Atlanta Fed GDP Now forecaster was at 2.1 percent for the quarter, up from 1.7 percent last week. The Atlanta Fed previously had one of the weakest forecasts, of just 0.3 percent for the first quarter, as of the start of last month.

Investors have been worried about a slowing economy, particularly after a string of softer data. Economists had expected that the first quarter would be softer than the rest of the year, with the government shutdown and winter storms affecting growth.

There has also been a growing belief that the soft economy would ultimately push the Federal Reserve into cutting interest rates one or two times this year. The Fed last month did an about face on its interest rate hiking forecast and eliminated two hikes for this year. It also said it would take its cues from the data.

While the Fed did not forecast cuts, the White House is now calling for an immediate cut of 50 basis points.The fed funds futures are pricing in one cut for this year and another for next year.

Among the positive data, construction spending rose by 1 percent in February, to a nine-month high after a strong gain in January. Retail sales fell by a surprising 0.2 percent, but January sales were revised higher to a gain of 0.7 percent, from 0.2 percent.

J.P. Morgan economists said the business inventory report for January was stronger than expected due to retailers building up stock. That helped boost overall inventories by 0.8 percent in January, and the December data was revised to also show an 0.8 percent increase.

Markets were encouraged by signs of life in China's manufacturing surveys Monday morning, and U.S. ISM manufacturing also improved, with the national factory activity index rising to 55.3 from 54.2 in February.

The much-anticipated employment report is released Friday, and economists expect about 170,000 new jobs. In February, there were just 20,000 jobs added, so the March report will be an important reading on whether the labor market remains strong, as economist expect.

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