The Kabbalists taught, a person can be involved all day in yichudim, intense kabbalistic meditations, this is what Chazal meant.
Still it was only once Hassidut was revealed that it become clear how to live this teaching of Chazal. These yichudim are a matter of using the whole world as a means of interacting with HaShem.
To me, this becomes the most clear when we realize that the whole point of prayer is to put aside all of our complications and recognize that HaShem is truly everywhere. The minute we wish to be with our Father, He's waiting there for us. Wherever we are, both in the physical and spiritual sense of where.
HaShem explains, that He fills the entire world. All the obstacles cannot be obstacles for HaShem, nothing prevents Him from doing anything. The obstacles are our obstacles. When we get past the obstacles, that is the essence of prayer. Finding some time to be alone with HaShem. Alone in all of creation, there's just you, and HaShem.
When we recognize this, then we understand what Chazal meant. Don't spend a minute of your day believing all those perceived obstacles out there provide any barrier or separation between you and HaShem.
Even our own sins that the Torah describes as separating between us and HaShem -- that's only from our side of things. From HaShem's side our sins certainly cannot keep Him from being with us. It's only us. If we don't want to have anything to do with "us" and all we care about is HaShem, so those sins cannot hold us back. That is the essence of Teshuvah, leaving the "us" behind in order to return to HaShem.
Instead of reading: "If only a person could pray the entire day," read: "If only a person could spend the entire day with HaShem."
HaShem spends every day with us. It's up to us to spend the day with Him.