Half of the Brazilian public sector is on strike for higher wages, but their prospects for success may be dimming as deadlines approach.

For months now, hospitals have been low on necessary staff. Traffic is backing up at security checkpoints. Infrastructure projects are stalled, police stations are understaffed, and many students are finding their classrooms empty of teachers.

In May of this year, university workers were the first to go on strike. Since then, up to 400,000 public sector employees have refused to clock in.

Demands vary according to sector; the BBC reports that some workers are demanding wage increases as high as 78 percent. Inflation is growing in Brazil, and these workers maintain that they are entitled to raises that can keep up with the cost of living.

But these public sector workers are indispensable to the running of the country, and their absence is putting a real dent in various sectors of the economy. By costing the government more money and thereby making pay raises even more unaffordable for the administration, these strikers could be shooting themselves in the foot.

Take the central bank workers, who are calling for a 23 percent pay raise. They're not completely out of the picture, according to a report from the Financial Times; the workers are still performing basic functions in order to keep the economy running. But one of the central bank's goals is to keep inflation down -- a long-term slowdown in performance there could result in higher costs of living, effectively weakening worker salaries in purchasing power.

Then there are the customs officers, whose absence at commercial ports has the potential to disrupt international trade. Inchcape Shipping Services, a major global shipping company that has operations at several ports on the Brazilian coastline, has said in a statement that "customs officers are disrupting major ports and ... the clearance of imported goods has slowed significantly."

With import revenues thus pinched, the national government will likely find itself less able -- and less inclined -- to swing a pay raise for customs workers.

Or take the security officers whose absence at international border crossings and airports threatens to hamper tourism, or to weaken the country's defenses against illegal drug and arms trafficking. At the huge Sao Paulo airport, some travelers are waiting in line for hours. And as for defense, some protesters poked fun at the situation by erecting a big sign on the thoroughfare between Sao Paulo and Rio de Janeiro.

"Police station closed," said the sign, according to the BBC. "Free passage for drug trafficking and arms."

Brazilian President Dilma Rousseff isn't laughing.

Rousseff seems wholly disinclined to give in to worker demands; she has actually called for wage cuts for more than 11,500 protesters. She has previously argued that any raises should reflect productivity -- which could mean that the longer civil servants stay on strike, the worse their odds become.

In fact, Rousseff sees a big-picture realignment that could put public sector workers at risk over the long term. She supports the privatization of Brazil's economy, which would involve giving corporations a greater role in improving the country's infrastructure. This month, she announced an auction of highways and railroads to private companies for about $65 billion, according to Reuters. And she promises to follow that with the increased privatization of air and seaports in the very near future.

Such plans may seem at odds with Rousseff's background; she is of the leftist Workers' Party and has denounced privatization in the past. Previous President Luiz Inacio Lula da Silva was of the same political bloc -- during his tenure, public sector wages rose much faster than did inflation.

Lula was a big spender, especially during his later years in office. But it is this extravagance -- compounded by a global recession -- that leaves Rousseff in a tough spot. Today, inflation is on the upswing and overall growth has slowed considerably, to a dismal 2.7 percent in 2011 and an expected 1.7 percent in 2012.

Over the next three years, Rousseff said, she is prepared to offer public sector workers a pay raise of about 16 percent. Workers complain -- and they may be right -- that such an increase would not be enough to balance rising inflation.

But the Rousseff administration just doesn't have much to give. Privatization is looking more and more like the cheaper solution, especially as workers' demands get steeper. Meanwhile, infrastructure projects are far behind and need to be addressed quickly in order to keep the country moving.

Rousseff gave workers a deadline of Tuesday come to an agreement and get back to work; she has threatened to take the issue to the courts if a consensus cannot be reached. The president has her own deadline to meet on Friday -- that's when the 2013 federal budget is due.

If the strike is not resolved by then, public sector workers may find themselves in a very tight spot.