Not an answer, but a clarification for OP: "lame duck" refers to a politician's final months in office, after a successor has already been elected, or when term limits guarantee that they will not be able to run for re-election. Essentially, it means "everyone knows you're about to be replaced, so you don't have much political influence anymore."
Ford was able to run for re-election in 1976, so the term would only apply during the last couple months of his presidency, after Carter had been elected.
I get the question you mean to ask, regardless of semantics. Just wanted to clear that up.
First off, I was 18 years old when Richard Nixon resigned, so I will try to avoid using my memory alone as I answer this!
In his short speech after taking the Presidential oath, Ford said: “Our long national nightmare is over.” This was used in headlines for many newspapers the next day. Two days before, many believed that Nixon was going to fight it out, requiring an impeachment vote in the House and a trial in the Senate. The general belief was that he would lose both by a large margin. While some probably would have loved to see this, most politicians were happy with the resignation because the country would be likely weakened by a trial and then removal. Effectively, Ford turned the page and received an incredible amount of positive feelings from the country. In addition, because he was well known in Congress, both parties showed a willingness to give him a chance, even with a Democratic Party majority in both the House and Senate.
However, the economy was in bad shape at this point. Inflation was in double digits, with interest rates also approaching 10 percent. The energy crisis was still going strong as OPEC continued to turn the screws with oil prices. Unemployment was on its way up, hitting over 8% in January 1975. No matter the support he received, the country was in danger of falling into further economic trouble.
Ford lost a great deal of his support a month after Nixon’s resignation when he gave the former President a full pardon on September 8, 1974. Nixon had not yet been charged with any crime, but Ford chose to issue the pardon right away. His approval rating (measured by Gallup) went from 71% when he took office to 50% after the pardon. It continued to go down, as low as 37% in early 1975.
By the time of the election campaign, Ford’s perceived weaknesses led to a tough primary season against Ronald Reagan. While Ford would win the nomination, the fact that he had such a strong challenger as a sitting President was very unusual. He was a heavy underdog to Jimmy Carter for most of the general election campaign, although he regained some support during the debates. He made a major error in the third debate when he stated that Eastern Europe was not dominated by the Soviet Union.
In the end, the popular vote was close at 50%-48%, but Carter won the Electoral College 297-240. Carter made his share of errors, which hurt his campaign, but as often happens, when the economy is bad, the sitting President usually gets the blame. Ford also vetoed 48 bills in less than 2.5 years (with 12 overridden). This is the highest number of vetoes since Eisenhower and hasn’t come close to being beaten since (Obama and George W Bush used the veto 12 times in eight years each!).
One of the things that consistently hurt Ford was the belief by some that he just wasn’t strong enough for the job. However, the numbers seem to show that if the economy had been better, he might have been able to get elected on his own, even with the Nixon pardon.