The long-awaited U.S. government plan to rid banks of money-losing assets has injected some desperately needed optimism into Wall Street after stocks hit 12-year lows earlier this month.

Judging by the 20 percent run-up in the benchmark S&P 500 index since its March 9 bear-market closing low, there appears to be a burgeoning consensus that some confidence maybe returning to the marketplace.

We shouldn't have to go back and test the lows, seeing the method by which banks are going to be able to remove toxic assets from their books, freeing up capital to lend, said Marc Pado, U.S. market strategist, Cantor Fitzgerald & Co in San Francisco.

But considering a bottom has eluded the U.S. stockmarket since the fall of 2008, there remains plenty of concern the recent spurt of gains could yet again be another false dawn.

The economic outlook remains shaky. Despite recent signs of life, the housing market remains mired in a deep slump and lending is stunted. Economists fear that unemployment could likely get much worse before efforts to jolt the economy out of the recession begin yielding results.

According to the latest Thomson Reuters data, first-quarter earnings for the S&P 500 companies should drop 35.6 percent from a year earlier. At the start of October, the estimated decline was 25.7 percent and 12.5 percent at the beginning of January.

Additionally, a key gauge of market fear, the CBOE Volatility Index , remains highly elevated, above 40, and inside a range at which every other rally since January has failed. Overall trading volume also remains tepid, suggesting a lack of broad conviction.

Given the many false starts in the equity market, VIX remains range-bound as investors aren't yet convinced that the recent rally is any different then the countermoves seen during the ongoing bear market, like the 25 percent rally in the S&P 500 from late November to mid-January, said Frederic Ruffy, options strategist at Web information site in New York.

Even so, the magnitude and the pace of the market's recent run-up in just 10 trading sessions, has some market watchers hopeful that Wall Street could add to recent gains.

We think there is a very good chance that the lows are in place for the stock market, said Bruce Bittles, chief investment strategist at Robert W. Baird & Co in Nashville, Tennessee.

It's probably due to excessive pessimism, a very oversold condition two weeks ago and the potential that the economy will show some improvement this summer.

Underscoring the bets about the economy is a recent upswing in crude oil prices, back above $50 a barrel. On Tuesday, U.S. front-month crude settled at $53.98 a barrel on the New York Mercantile Exchange.

Anybody who is a long-time investor should have been buying the entire time everybody was panicking, said Michael Williams, chief investment strategist at Tocqueville Asset Management.

Bear markets end when they start deciding to go up in the midst of continuing and probably worsening news. Once we know we can continue to see poor news be greeted with either much less selling or a rally, then capital is telling you it has priced-in a worst case scenario, Williams said.

The market jump from the 12-year low marks only the fifth time since 1929 that the broader market has had such a big bounce in just a short period of time, according to market research firm Birinyi Associates.

In Tuesday's trading U.S. stocks ended lower, however, as investors paused to reassess if the latest government measures will be able to sustain further rallies akin to Monday's surge that drove the S&P 500 up 7.0 percent and lifted the Dow Jones industrial average up almost 500 points.

Anxiety levels remain elevated, Ruffy said.

U.S. Treasury Secretary Timothy Geithner, who has come under fire for his handling of the financial crisis and the use of government bailout funds to pay big executive bonuses, on Monday spelled out the details of public-private partnerships to help rid banks of soured assets, offering generous government financing for them to do so.

(Additional reporting by Doris Frankel and Rodrigo Campos)