Act I of Death of A Salesman opens up the door to Willy's mind and personality, especially when he begins to have his vivid flashbacks of better times gone by.
When it comes to the Chevy we find that, in one same conversation, Willy openly contradicts himself about the car's efficiency and service.
When Willy is having a flashback about better days, he remembers how he and the boys acquired the car, their home, and were basically living up the American Dream. Those were the days when Willy was still young and hopeful. Having the car and the house were indicators that he had finally "made it".
Linda: How'd the Chevy run?
Willy: Chevrolet, Linda, is the greatest car ever built.
This is the reaction that Willy gets towards his All-American car when things are going well and when he feels that he has finally succeeded in life: he is married, has a home, has kids, is "well-liked", has a sales job, and...he has his dream Chevy.
Yet, in that same conversation, Willy comes back to the present. Here he is, 63 years old, still a mediocre salesman, making less than ever, his sons all grown and doing not-so-well. When he remembers the Chevy back then, Linda is (in the present) relating to Willy all the debts that they owe now. Among those things they need money for, there is the Chevy. It had to get its carburetor changed and Willy owes money for that. Here, the attitude changes.
Willy- I'm not going to pay that man! That g***amn Chevrolet! They ought to prohibit the manufacture of that car!
Here is reality: The Chevy, like Willy's American Dream, will not last forever and is now old, used, and broken down. It even needed some replacements. This allegorical element shows how Willy's life has actually gone downhill with time, instead of the other way around. Willy knows this, and this is why, when things are good, the Chevy is a great car. When things are bad, the Chevy (much like his dream) is a disgrace.