LKZ,
It is as I suspected and initially recommended, and as Tag also suggested...
You have an OBLIGATION to say Shema whether you own Tefillin or not. The statement of Rabbi Ulla must be taken figuratively, not literally, as there is no halacha that one who says Shema without Tefillin are liable for lashes (or the punishment for bearing false witness). This is a spiritual concept...
Look at the wording in this page of gemara:
http://halakhah.com/berakoth/berakoth_14.html'Ulla said: If one recites the Shema' without tefillin it is as if he bore false witness against himself.16 R. Hiyya b. Abba said in the name of R. Johanan: It is as if he offered a burnt-offering without a meal-offering and a sacrifice without drink-offering.
It is
AS IF he bore false witness, he did not actually commit the transgression but only on a spiritual level... A man is not liable to punishment in this case.
But my Rabbi advises as I do, to get Tefillin when you have an opportunity. Please seek out a local Chabad near you, contact the Rabbi, and he can find you Tefillin which should be able to be in your budget (and if not he may be able to find sponsors for you).