Federer is just 2 third-round performances away to complete a full decade of winning his first 2 matches.
Round / Fed's best / Best excluding Federer
R128 52* 56 Ferreira (Edberg 54)
R64 38* 29* Ferrer
R32 38* 28 Lendl
R16 33* 28 Lendl
QF 33* 14 Lendl (Djokovic 13*)
SF 23 10 Lendl (Djokovic 9*)
F 10 7 Crawford
W 3 6 Budge
* = active streak
record in bold
On schedule to hold the record for each round except the most important, wins.
I consider that Connors has 27 straight slam quarterfinals between Wimbledon 1973 and Roland-Garros 1983 : of course he didn't take part in the Australian open and in Roland-Garros for some time, but if you exclude all those who didn't play the Australian open, you exclude many players, especially in the 70s.
Moreover, Connors was not a claymug at all, there's no reason to think it's an unfair advantage to him to discount his absences in Roland-Garros.
For the semifinals and for the same reason, Connors is also second in my eyes with 11 semifinals between the US Open 1976 and the US Open 1980.