Starting with a definition of double down in its metaphorical sense:
(phrasal verb, US)
strengthen one's commitment to a particular strategy or course of action, typically one that is potentially risky
He decided to double down and escalate the war.
The third quarter of the year saw central banks doubling down on the quantitative easing approach.
As regards politicians, at least, doubling down often only amounts to a mere repetition of words, restating a position, or perhaps a refusal to change course or to admit that something was wrong. The risk they are taking, implied by the blackjack analogy, is, as far as they're concerned, usually intangibles like loss of face, reputation, political capital etc. (although, as one of the example sentences above shows, this often also involves putting lives in the balance).
With that in mind, depending on the precise context, there are other words and phrases you could substitute - although all have their own distinct meaning and nuance. None of them is a straight swap for double down but there are situations in which one or another will work in its place.
to increase the costs, risks, or considerations involved in taking an action or
reaching a conclusion
The Libyan allegations raised the stakes in the propaganda war between Libya and the United States.
This is, of course, another gambling metaphor, and is relatively close in meaning to double down. It involves a clear and explicit increase in risk, much as double down does.
However, while one can double down on something (a particular allegation, perhaps, in the example above), the stakes are raised in the context of some overall metaphorical game. You might raise the stakes by alleging something, if you need to get specific, or just let the allegations raise the stakes, like in the example.
stick to one's guns (phrase, informal)
refuse to compromise or change, despite criticism
We have stuck to our guns on that issue.
As a practical matter of swapping one phrase for the other, stick to one's guns is perhaps the closest match to double down, although the sense is not so much of deliberately raising the stakes, but rather a dogged refusal to budge. (In terms of flavour, a gambling metaphor doesn't sound too far off a gunfight one, either - they are in the same ballpark, if not the very same saloon.)
Also, although the dictionary I have quoted lists the phrase as informal, this strikes me as a rather conservative view; it is of a suitable register for journalism.
dig in one's heels (or toes or
resist stubbornly; refuse to give in
Officials dug their heels in on particular points.
Very similar to the above, this is an obstinate rejection of compromise or change of direction or stance. (Politicians, beware: if you dig in your heels when they dig up the dirt, you might dig a hole for yourself.)
While pressure and criticism are implicit, any increase in risk is not emphasised with this phrase.
refuse etc. to back down
is defined as:
withdraw a claim or assertion in the face of opposition
Party leaders backed down and rescinded the resolution.
Example sentences from the same dictionary involving a refusal to back down include:
She makes her opinion known, never backs down and never lets up.
However, neither the French nor Austrian governments showed any sign of backing down from their proposals.
The president also said he has no intention of backing down from his plan.
As the example sentences show, this phrase is frequently used in political contexts. Again, the sense of an increased danger or risk that double down can often carry isn't present here.
Here's some adjectives you might want to throw in the mix (possibly as adverbs) to help get the full flavour of double down: