Richard Nixon, wasn't a very popular President his first couple years as President, with the Vietnam War that he inherited and with the anti-war movement that was going on as well. President Nixon inherited a lot from President Johnson when he became President. And made a lot of tough decisions, like expanding the Vietnam War in an attempt to bring North Vietnam to the negotiating table. Which in the end worked. But he paid a heavy price for it politically and wasn't really a lock to get reelected until the spring or summer of 1972. After the Nixon Administration reached and agreement to end the Vietnam War with North Vietnam.
President Nixon, also had two successful foreign policy trips to Russia and China and opening up relations with both countries. The first American President to arrive in either country. Dick Nixon was about twenty years ahead of him time on foreign policy. Whether you like him or not or are in between, you have to give him credit for that. He's one of the most intelligent politicians and President's we've ever had. And for that reason he could see how things were developing and how they were going to look in the future. And this "Dump Nixon" movement in the Republican Party must of been a reaction from I guess the libertarian wing of the party.
Republicans who believed the Vietnam War was a mistake and one of the reasons why they elected Dick Nixon was to end the Vietnam War. But he expanded that war before he ended it. They must been the people behind the "Dump Nixon" movement. And thats not what they were looking for, but a complete end to the war. Its a huge risk to take on your own President the leader of your party, when he's in his first term. Which is exactly what President Nixon was by 1971. Because again President Nixon was no lock to get reelected in 1971, he wasn't very popular at this point.
Also the Democratic Party still has solid majorities in Congress. Both in the House and Senate and losing the presidency in 1972, which of course didn't happen, but had that happen, the Republican Party would once again find themselves out-of-power in the Federal Government. Just like in the 1960s when Congressional Democrats added to their majorities. Republicans had to retain the White House in 1972 to further their momentum that they made in the South in the mid and late 1960s. I wasn't aware there was a "Dump Nixon" movement. I didn't believe Republicans ever did things like this. The only other time I'm aware of this happening was in 1992. When Pat Buchanan and his supporters took on President George H.W. Bush and ran against him in the Republican primary's and had some success. This kinda thing generally happens in the Democratic Party, when the Far Left believes the President is not progressive enough like today.