The heart of the problem is that the government cannot create jobs because its only source of income is to take it from other people. If you work for the government you are being paid with other people's money. At best, the government redistributes jobs rather than creating them.
That doesn't stop the left. For some reason, they only see half of equations. They see the government hiring people but they don't see the hardships caused by increased taxes. In fact, they celebrate paying taxes. Remember Biden's statement about taxes being patriotic?
This is the same debate that we keep having about Social Security, Medicare, and Medicaid. They have trust funds but these funds have to be paid from the general fund which is currently borrowing $0.40 out of every dollar spent.
There is also the question of what these jobs would be. "Infrastructure" keeps being tossed around but President Obama already admitted that there is no such thing as a "shovel ready" job. An major investment in infrastructure now would not see any real job creation for years. It might not help unemployment much, either. A big problem in the current economy is the mismatch between job openings and job seekers. An unemployed real estate seller might not take a construction job, even if one was offered. This is especially true when unemployment benefits go for almost two years.
Government can also "create" jobs through regulation. A requirement that every restaurant have an in-house health inspector would create a lot of jobs but it would also put a lot of marginal restaurants out of business. This is a variation of the "broken window fallacy". If someone breaks all of the windows in a village it will create work for the glaziers but repairing the windows would divert money that would have been spent elsewhere, depriving all other parts of the economy.
The most that government can do is to try to get out of the way. It needs to keep regulations and taxes down to the minimum and provide certainty. Currently the EPA is increasing regulations and Obamacare has created uncertainty about the cost of future employees.
In the 1980s, Reagan cut taxes on everyone and slowed the growth of government. The economy soared. In contrast, Obama has temporarily cut taxes on the non-rich while increasing the cost of doing business and openly calling for more taxes. Then he wonders why businesses are hoarding money.
Related mini-post: How Government Gets Its Money
As I said, the government's only source of income is other people. The most direct source is taxation. This is often combined with social policy. That is why half the country pays no income tax while Obama desperately wants to raise taxes on "the rich", AKA "Millionaires and billionaires." Obviously, money paid to the government in taxes cannot be used elsewhere.
The government can borrow money. In theory this will be paid back (with other people's money). In practice, the government pays current amounts due by borrowing more. It also pays interest on the debt. There is a very real danger that the interest on the debt will swallow the rest of the budget within a decade. Any new jobs bills would probably be paid for with borrowed money.
Finally, the government can print money. This still takes other people's money but it does it indirectly. Every dollar that the government adds to the money supply reduces the total value by that much. This shows up as inflation which is currently increasing and declining exchange rates. Even if the government does not take your money, it does not go buy as much as before so your total buying power is reduced.