The S&P Case Shiller index of housing prices rose 0.3% in January on a seasonally adjusted basis. On an unadjusted basis, which does not include data on foreclosures, the index fell 0.4%. The decline in the unadjusted price is double analysts’ expectations of a 0.2% decline.

Housing prices started to rebound in the fall of 2009 as buyers rushed to take advantage of a federal tax break on home purchases. Even though Congress eventually extended the tax break to the end of April 2010, the momentum that had moved prices upward was broken. Since November, housing prices have declined every month. That has caused plenty of headaches for builders like Toll Brothers (TOL) and other housing stocks.

The data is improving on housing prices, but at a snail’s pace. One analyst quoted in the New York Times noted that it is “only a matter of time before the index records a double-dip in prices.”

If that double-dip materializes, it will be the result of the end of the tax break for home buyers and the end of the Federal Reserves massive infusion of cash in mortgage-related debt. The Fed expects to stop buying mortgage debt at the end of this month, having spent nearly $1.25 trillion in an effort to shore up housing prices.

Clearly the Fed wants private investment to return to the mortgage market. Failing that, the central bank has indicated that it begin buying mortgage-backed securities again if the market doesn’t recover.

Some recent signs of rising consumer confidence have offered new hope that housing prices will continue to advance. Home furnishings companies like Bed Bath & Beyond (BBBY), Williams-Sonoma (WSM), Kirkland (KIRK), and Pier One Imports (PIR) have either reported good gains in the past quarter or are expected to. (Check out a breakdown of home furnishing stocks here)

Auto sales, while still soft, are also rising. Just as in housing, though, sales incentives appear to be driving the results at Ford Motor (F), General Motors, and Toyota Motors (TM).

The consumer confidence index is again above 50, but it wavers depending on unemployment news.

A sustainable upward trajectory in housing prices probably depends as much on unemployment data as it does on mortgage rates. While the federal government has been propping up the housing market, sales have improved. When the props are pulled out, though, is the sales price recovery going to continue or will it collapse?

If unemployment numbers do not continue to improve, it’s hard to see how housing prices can continue to improve. Federal incentives for home buyers cannot continue indefinitely, and the Federal Reserve cannot afford to keep buying piles of mortgage-backed securities forever. Consumer confidence must return in force, and the only thing that will cause that to happen is less unemployment.

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