The Left isn't a monolithic entity but I can talk as to the CPUSA's reactions.
Generally, they were opposed. During the Depression, they saw it as a small concession to save Capitalism, but by the War they had abandoned that stance in favor of a United Front against Fascism.
Many communists saw the Depression itself as a fulfillment of Marx's theory that capitalism would inevitably consume itself. Marx was one of the first economists to write about the 10-year boom and bust cycle, but believed that this cycle of production and 'overproduction' would inevitably destroy the entire system. According to theory, capitalists look only towards the short-term profits and undercut labor costs as a way of achieving this. Produce more and pay less. Their workers are also their consumers, however, and the prices will regularly become too much to afford - what he termed overproduction, and many Keynesian later called 'underconsumption'.
When the overvalued stocks fell through the floor in 1929, anxiety swept the public and millions tried to pull their cash from the banks all at once. This forced them to recall their loans and this in turn forced businesses to close, and put millions into debt. Merchants and farmers burned their own crops and slaughtered their livestock to artificially increase the price and try and stay afloat. Millions were put out of their jobs, often blacks before whites. At the same time that the consumer base was being destroyed, millions were being put out onto the streets and into 'Hoovervilles'. By 1933, fully one quarter of the working population was unemployed, and in many neighborhoods unemployment was over 50%. Entire families incomes disappeared, and the prices just kept increasing.
For many communists of the time, it looked like Marx was being proven right - global capitalism was on its last leg.
The CPUSA grew tremendously during the depression, reaching their peak of 85,000 members in 1942 - just as the United States entered WWII.
The first of the three reasons for this was the creation of the Unemployment Councils in 1930. Day-to-day, the Unemployed Councils staffed soup kitchens, flop houses, and raised demands with the administration over sanitation and bad food. They stepped in to prevent evictions and keep gas on. And through that work, they were able to "raise consciousness" and become embedded in the communities they served, earning their trust and winning them over to a more radical politic. They organized hundreds of thousands of the angry poor not just for demands of new employment, but an end to employment entirely. The CPUSA especially organized across racial lines, across gender lines, and the Unemployed Councils did the same, organizing white and black workers, men and women, together.
The second was their organizing across racial lines and of black workers in particular. James W. Ford ran as the Party's vice presidential candidate for all three years of 1932, 1936 and 1940 - being the first African American to appear on a presidential ballot in the 20th century. The issue of racism was made central to the party's work. As Harry Haywood details in his autobiography [1], this wasn't entirely by the CPUSA's own choice, as most of the membership saw the question of racism as secondary to that of class. The Communist International refused to regard it as mere discrimination, however, and the CPUSA were made to put a significant focus on that issue and treat it instead as one of national oppression. To quote from their Election Platform for 1936:
The Negro people suffer doubly. Most exploited of working people, they are also victims of Jim-Crowism and lynching. They are denied the right to live as human beings. [2]
This work lead to the creation of an active Southern Party that was almost entirely black, and a regional newspaper. The Party became involved in the case of the Scottsboro boys and lead rallies against their incarceration across the country. [3]
The third reason was their involvement in labor organizing during this period - especially in the Congress of Industrial Organizations, a union federation that was expelled from the American Federation of Labor for 'industrialism' (that is the organizing across an entire industry and not simply by trade) and for being communist lead. The AFL opposed strikes as anything but a last resort, and had been unable to win any through the Depression, until the 1934 strikes of the West Coast Longshoremen, Minneapolis Teamsters, and Auto-lite. All lead by Communists, and expelled from the federation in 1935 over this issue (and punching a union rep in the face during an argument over it). The CIO managed not only to maintain its shops through the depression, but to actually grow and win a dozen other strikes across the country. The CPUSA maintained control of the new federation through the rest of the 30's and enrolled many of the Unemployed Council workers on their rosters, attempting to link the interests of the employed and unemployed and grow picket lines. [4]
1936 was also the highest that they ever polled in an election, only receiving 0.26% of the vote [5] - and although Communists have historically denounced elections as a means to real progress, they have upheld them as a good measure of popularity. FDR passed the New Deal in a context where Communism was on the rise, and many communists saw this as an attempt to push off that inevitable doom of capitalism, and to undercut their growing movement by giving out quick-fixes to a deeper issue. They saw it as an attempt to save capitalism.
To quote from the Platform, again:
Roosevelt is bitterly attacked by the forces of reaction. But he does not fight back these attacks. Roosevelt compromises. He grants but small concessions to the working people, while making big concessions to Hearst, to Wall Street, to the reactionaries.
In 1937, The Party adopted a United Front against fascism - openly declaring the need for an alliance between socialists and liberals. The 1936 platform stands as a middle ground between their previous opposition to FDR and revolutionary stance, and later tactic of the United Front. The platform both decries the New Deal and fascism - both FDR and Hoover, but in a way that Hoover is denounced as a far greater evil and FDR as merely compromising with the Right.
[1] Black Bolshevik, by Harry Haywood.
[2] https://archive.org/details/CommunistElectionPlatform1936/page/n3
[3] Hammer and Hoe, by Robin D.G. Kelley
[4] The CIO 1935 -1955, by Robert H. Zieger
[5] https://www.marxists.org/history/usa/government/elections/president/timeline.htm
Follow-up question: How did the Soviet Union view the New Deal? Did they see it as a step towards communism?
As u/crying-child notes, the Left wasn't a monolith. The Socialist Party was particularly contentious - with divides between labor and academy, reformers and militants, and the like. It's also worth noting that the New Deal was so successful that it managed to attract a lot of moderates and intellectuals on the Left towards the Democrats, who tired of the contentiousness between the Old Guard and the younger Militants. But we can look at it the New Deal through the eyes of some of the Socialist Party's leaders - like perennial presidential candidate (and former Presbyterian minister/Social Gospel proponent) Norman Thomas.
Thomas believed that the New Deal put through a weaker version of nearly the entire Socialist Party of America's platform. He also believed the New Deal got more done than he probably could have, and in a very short period of time. And Thomas respected this, thinking that although it was "hopelessly inadequate" it was a start in a good direction and even conceded that were Thomas president, he would have used his first hundred days in the same way Roosevelt did. He, and other Labor leaders like Abraham Cahan honestly considered making Roosevelt a kind of honorary member of the Socialist party - if only he would consider nationalizing banking and coal-mining.
Thomas had a two big complaints about the New Deal, though. First, predictably, that it wasn't radical enough. It was ameliorative, but it didn't actually address the core philosophical and ethical problems of America. The New Deal for all its benefits preserved and protected capitalism, albeit in more of a state-capitalism form that many feared was similar to fascism. And second (and this betrayed part of why the Old Guard socialists, particularly in the Midwest really distrusted him) - the New Deal did not empower people of color. Roosevelt's administration, and the New Deal program maintained the unjust racial status quo - in particular within the agricultural aspects of the New Deal.
So from Thomas' perspective, the New Deal was really a mixed bag. It did a lot of what Thomas really wanted to do. In fact, it did more than Thomas could have possibly done for the poor. It also didn't do enough, and its blindspots were very concerning. In the end, Thomas (erroneously) blamed the New Deal's successes for the collapse of the Socialist Party. That might be part of the truth, but it's certainly not the whole of it.
Source: Bernard Johnpoll Pacifist's Progress: Norman Thomas and the decline of American socialism (Quadrangle Books, Chicago: 1970) 87, 101-105, 172-174, 289
While we wait for a quality answer that follows the rules, there is a solid answer by /u/kieslowskifan from 11 months ago answering if the USSR (and the Nazis) viewed the New Deal as socialist.
As a follow up, what did communists and socialists think of FDR's Second Bill of Rights?
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