If G > T then there's a budget deficit. This injection into the economy will boost demand and thus create jobs (demand for labour is derived from demand for the product)
Thus the government can create jobs.
Government spending of debt money does not result in any net creation of jobs at all. It only confiscates wealth from private citizens and forces them to pay for centrally-planned jobs that the real economy usually neither needs nor benefits from.
Consider three people living in an island, running their own tiny economy. Bob, Sarah and Charlie are all farmers who grow their own food, making an honest living by working 8 hours a day to create the food, clothing and shelter they need to survive.
One day, Charlie decides he wants to be the Governor of the island. He tells Bob and Sarah that as Governor, he'll bring wealth and prosperity to them both. Initially, that sounds good, so Bob and Sarah agree to elect him Governor.
Then it turns out that the Governor is busy governing things on the island (i.e. deciding what everybody else should do), so he has no time to grow his own food. So he initiates a 50% tax on the productivity of Bob and Sarah, confiscating their food, clothing and resources in order to provide those items to himself without actually having to work for them. (This is a key function of government: To confiscate wealth from those who really work and redistribute it to those who pretend to work.)
Now, Bob and Sarah each have a choice: They can either work twice as much in order to pay their tax and still have enough to survive, or they can quit working altogether and hope to get aid from the government.
Sarah decides to work twice as much, so she starts working 16 hours a day, earning enough to pay the taxes to the Governor while still having some remaining food to feed herself and her family. Bob, on the other hand, decides he doesn't want to work 16 hours a day and would rather do nothing and apply to the Governor for "public assistance."
So now on this island of three people, where each of the three people used to work to feed themselves, only one person is working (Sarah), and the other two are living off the wealth that's being confiscated from her efforts.
One day Charlie, the Governor, says he has a solution! He says he will write a series of IOUs to Sarah in exchange for an extra portion of her food and other belongings. Using that currency borrowed from Sarah, he says he will "create a new job" for Bob and "end unemployment on the island."
Sarah reluctantly agrees and turns over the fruits of her labou to the Governor, who invents a job for Bob. "Bob," he says, "We need to build a bridge across this island!" And with the wave of his hand, he puts Bob to work creating a bridge (that nobody needs) while getting paid by wealth that has been confiscated from the only person on the island still working (Sarah).
So now we have ONE person actually doing productive work, a second person living off the confiscated wealth of that person (the Governor), and a third person working a useless job that's now paid for by the first person as well. This means we have ONE person supporting THREE. And while the island is at "full employment," two out of three people are actually doing jobs that don't materially contribute to the wealth and abundance of island's residents.
And the best part? Guess who gets to work even more to pay back the IOUs that the Governor traded with Sarah? Well Sarah, of course, because those IOUs are public debt paid back by taxpayers.
The problem on this little island is NOT that insufficient money is being spent on an economic stimulus program; the problem is that the island suffers from too many bureaucrats and too much debt spending.
Fire the Governor and the government worker, shrink the size of government and get everybody back to working their own gardens, growing their own food and supporting their own families. Productivity on the island would triple, and people would have to get back to doing honest, productive work instead of living like parasites off the efforts of taxpayers.