The move was popular at the time. In fact its popularity caused Justice Roberts to switch his vote, What is often called "The switch in time saves nine". If Justice Roberts had been a member of the "Four Horsemen" of the Supreme Court. All four of the "Horsemen" voted against the New Deal and the Social Reforms of the New Deal till Justice Roberts switched his vote to uphold various parts of the New Deal as Constitutional. This happened in an opinion released within two months of FDR proposal to increase the number of Supreme Court Justices, but seems NOT to have been the reason (Justice Roberts told the then Chief Justice Hughes that we was voting to switch do to how bad the economy was getting in 1938 and something had to be done, and the New Deal was better then the Laissez-faire the GOP right wing had been proposing, a right wing Roberts had long been a part of).
Furthermore another member of the Four Horsemen would resign within a month of that switch (Permitting FDR to appoint Hugo Black as his replacement), reducing the four horsemen to two, and increasing the Liberal wing of the Court from three to five ( you include Roberts who then voted to uphold the New Deal till he resigned in 1945 but stayed otherwise a good conservative, to such an extent that he had become isolated from the rest of the then liberal court).
The Court Packing deal was more political posturing for with the court's switch (The horsemen reduced to two then to none within two years) it ceased to interfere with the New Deal reforms. Thus it became more a way to attack FDR then to defeat the New Deal. When that became clear even to FDR he withdrew the proposal. The Democrats would retain control of the House and Senate in the 1938 election (With some loses in both houses) but FDR would win again in 1940 and 1944 bring with him large Democratic Majorities (Through still dependent on Conservative Southern Democrats for a Majority). The GOP will have to wait till 1946 to win control of the House and Senate (And then only hold it till 1948 when the Democrats would win all three position). The GOP will win all three positions with the Election of Eisenhower in 1952, but lose the House and Senate in 1954 and the Senate will stay Democratic till 1980 and the House till 1994 (Through the 1980 election the Democrats only held the Majority based on those same Southern Conservatives, most were defeated or out by 1994 and are no longer part of the Democratic Party).
For more on the original Switch:
http://en.wikipedia.org/wiki/The_switch_in_time_that_saved_nineMajority Parties of the Senate since 1787:
http://www.senate.gov/pagelayout/history/one_item_and_teasers/partydiv.htmList of majority leaders of the House (i.e. who controlled the House or Representatives:
http://clerk.house.gov/art_history/house_history/leaders.htmlUS House of Representatives "History page":
http://clerk.house.gov/art_history/house_history/index.html