likely

Likely is most often used as an adjective, meaning probable, (opposites unlikely / improbable). If something is likely, it is probably going to happen:

• The most likely cause of the fire in the stadium was an unextinguished cigarette
  
  
• The most likely outcome to the investigation is that the stadium will have to be rebuilt.

With the modifiers most, quite or very, likely is also sometimes used as an adverb, meaning most probably:

• They'll quite likely invite you out to eat in a restaurant when you're staying with them.
  

it's likely that + clause

Likely is quite often used with it as a preparatory subject:

• It's unlikely that this afternoon's session will last very long. It should be over by five o' clock.
  
  
• It's more than likely that I shall see Chris in Cambridge. I am almost certain to bump into him, in fact.

be likely to + infinitive

As an alternative, we can use the be unlikely to + infinitive construction with a normal subject, but probable cannot be used in this way:

• This afternoon's session is unlikely to last very long.
  
• I'm unlikely to be back late from the meeting.
  
• Are you likely to be staying in when you get back?

It is this realisation of likely that is used in your example, Reinhard:

• The authorities are likely to be hard pressed to respond to the disaster.

Note that if we wanted to use probably as an alternative in these examples, it would need to re-phrase them as follows:

• This afternoon's session will probably finish quite early.
  
• I shall probably be back quite early from the meeting.
  
• Will you probably stay in when you get back?
  
• The authorities will probably be hard pressed to respond to the disaster.
  

hard pressed / pushed

If you are hard pressed or hard pushed to do something, you experience great difficulty in doing it. Being pressed suggests being under pressure:

• It seems to me that the Labour government will be hard pressed to win the next election.
  
• We were hard pushed to complete all the preparations before the guests arrived.

Use of the adverb hard here suggests a lot of force being used against you. Note that hard also sometimes suggests physical force:

This door is inclined to stick, but if you push it hard, it will open.

pressed for time / money / etc

Pressed also collocates with time and money and other ideas in a similar way to hard pressed, suggesting difficulty:

• Are you pressed for time? If not, I suggest we have some lunch.
  
• This one's worn out. Why don't you buy a new one? ~ I'm a bit pressed for cash at the moment.
  
• It's not really her subject, but she says she could teach beginners Spanish if we're really pressed.