Stephen Hester, boss of the 81% taxpayer-owned Royal Bank of Scotland (RBS), is to receive a £963,000 bonus.
Deputy political editor James Landale told the Today programme that, because the government is the main shareholder, they have a "very difficult argument to make" to convince the public the bonus is warranted.
Behind the scenes, he said, the government has been an active shareholder by putting pressure on RBS not to award bonuses worth over £1m.
Business editor Robert Peston said that one of the reasons the government is staying quiet may be because the board of RBS "sent a strong signal that their position would have been undermined" if they were forced not to give a bonus.
They warned they might have a legal obligation to quit if the bonus was blocked, he said.
However, shadow business secretary Chuka Umunna said he "would not have paid out any bonus" to Stephen Hester in the circumstances.
He pointed out that because this bonus has been given in shares, the actual amount that Mr Hester may receive could be over £1m.
The public would be "flabbergasted" that the bonus had been blocked, he said. While he had done a good job, "that's what most of us do in our jobs".
Get in touch with Today via
or text us on 84844.