Let me begin by saying that congress was more important than FDR in passing the New Deal in many ways. While the president and his campaign for government intervention in regards to the Great Depression was the face of the New Deal, the body, implementation, power, and structuring of the bill came from a solidly Democratic congress (both in the Senate and House). The New Deal swept in fast, promising the famous 3 R's: Recovery, Relief, and Reform. In what can only be described as a huge break with past American ideology, the Federal government redefined its role in the lives of everyday citizens. FDR even suggested it was the role of the government to grantee all men the right to a certain standard of living.

Now, here is where I get a little more specific on your question. The Civilian Conservation Corps (CCC) and Works Progress Administration (WPA) were part of the “Relief” effort. Since the WPA was a much larger project, I will focus on that. The WPA combined private enterprise together with federal and state government subsidization (between 20-30 % of overall costs) in order to complete a vast array of public work projects. Since the WPA was not 100% paid by the government, and because it put people to work instead of just giving them a dole from Washington, it was seen (much as the CCC) as a good program and it wasn’t hugely at odds with the constitution in regards to the power of the government. The CCC and WPA would continue until the beginnings of World War II when war production and military mobilization would render these programs unnecessary.

By 1936 however, the United States Supreme Court had struck down the Agricultural Adjustment Act (AAA), National Industrial Recovery Act (NRIA), and other similar organizations that the Supreme Court regarded as unconstitutional federal intervention in private business that didn’t cross state borders. This would set into motion FDR’s jury loading scandal and the Second New Deal, all reactions against the Supreme Court’s power which FDR saw as overly conservative, obtrusive, and out of touch with the harsh reality the United States was then facing.

So I will try and end this somewhat harmoniously. The answer to your question is though the Great Depression would stretch on until the beginning of the Second World War, many people would keep faith in the New Deal and its later reincarnations/alterations. FDR was able to win a landslide reelection in 1936 with 60% of the vote (losing only Maine and Vermont), thus demonstrating his mass popularity. Ultimately, it was the Supreme court that shut down many of the New Deal’s programs, stating they exceeded the Legislature’s power to regulate the American economy and its businesses.

Long Term, the Social Security Act, Wagner Act (right to unionize), and the Federal Deposit Insurance Corporation [(FDIC) which insured a certain amount of money from loss in banks] would be the most powerful and long lasting legislation from the New Deals. While the CCC and WPA did help to some extent, their main power came from boosting moral and invigorating Americans, showing many US citizens the government was at least trying to assist them. They were never overly unpopular and their death was a result of the United States’ growing economy, not due to unpopularity or the Supreme Court.

Alter, Jonathan. "The Defining Moment: FDR's Hundred Days and the Triumph of Hope" (2006).

Mettler, Suzzane. "Dividing Citizens: Gender and Federalism in New Deal Public Policy" (1998).

Follow up question: Historically, does support for these kinds of programs have a connection to the economy? For example, the new deal was popularized as a way to fight against the Great Depression, but after the modern 2008 financial crisis, we've seen a rise in populism and support for opposing new deal like programs in the tea party and other political groups. I'd be interested to know also if there is a consistent trend with the world or if the U.S. is different, but if that broadens the scope of the question too much to be practical, limiting the answer to the U.S. is just fine.

The WPA and the CCC were ended during WWII because of war time employment and the draft ended the issue of unemployment.

During the 1970s chronic inflation and rising unemployment led to a New Deal like push for full employment legislation, with organized labor teaming up with liberal Democrats to create the Humphrey-Hawkins full employment act. The idea was to incorporate the economic demands of organized labor with civil rights activists demands for economic opportunity for minorities. It was to be a post-Civil Rights New Deal that could ease the tensions between a white working class which was being threatened by rising unemployment and inflation, and the civil rights movement which wanted a greater share of shrinking economic opportunities. By 1976 the bill started to take its ideal form. The plan was to use nationally coordinated economic planning at high wages and a mandated right to a job for every American. Full employment was to be at a 3 percent unemployment rate. Local planning councils would be able to initiate projects to satisfy community needs. It was an audacious idea. The bills sponsors got the AFL-CIO and Congressional Black Caucus together to hammer out the details and make compromises. the bill was part of the Democratic party platform in 1976 and it was widely supported by grassroots party activists, as well as civil rights activists and organized labor. Many in the liberal-left faction of the Democratic party were skeptical of Carter's intentions particularly labor, because he ran for the nomination without the full support of the major unions.

The bill never really happened, although it was signed into law by Carter in 1978 by that point it was a shell of the 1976 version. Carter was more concerned with fighting inflation than implementing collective planning for full employmen. More conservative Democrats in Congress fought to reduce the most left-liberal portions of the bill. Instead of a new New Deal, what came out of the legislative process was basically a call to reduce the trade deficit, the budget deficit, and manage money supply to fight inflation. A far cry from the demands of the left-liberal wing of the Democratic party. Full employment just wasn't universally appealing in the late 1970s. Many middle-class Americans were more concerned about inflation than unemployment. Many economists were deeply confused about how to tackle high unemployment while fighting inflation. The Carter administration, and enough Congressional Democrats, basically made a choice to use monetary policy (hiking interest rates to reduce the money supply) rather than collective economic planning.

As a side question: my grandfather told me that in the CCC and the WPA, they would have literal make-work jobs, where they would have a day crew dig a ditch and a night crew fill it in. Did this really happen? Were there really jobs that accomplished nothing but to pay the workers?