Labour, more than half way through its third consecutive term in office, has a working majority in parliament of 67.
Field may be able to force through the tax compromise if opposition parties support the amendment.
Defeat on the tax issue could trigger a confidence vote, potentially threatening to bring down Brown's government, but dissident Labour lawmakers would be likely to rally round Brown in that case.
Finance minister Alistair Darling told a meeting of around 50 worried Labour lawmakers on Tuesday that he would find a way of addressing their concerns in time for his pre-budget report, expected in October.
Any solution would apply to the current financial year, a Treasury source said, a key demand of the Labour dissidents.
The pledge was enough to convince some Labour lawmakers at the meeting. Ronnie Campbell told Sky News he had changed his mind about voting against the government.
"I've got that commitment this afternoon from Alistair Darling that he will make it up to people who have lost out and that is good enough for me," he said.
Commentators said Brown would face repeated battles with dissident Labour lawmakers over the coming months as his party continues to lag the opposition Conservatives in opinion polls.
One glimmer of light for Brown came on Tuesday in an opinion poll in the Guardian newspaper that showed Labour clawing back some ground from the Conservatives compared with a month ago.
The ICM poll put Labour support up five points to 34 percent with David Cameron's Conservatives down three points to 39 percent. The third main party, the Liberal Democrats were down two points on 19 percent.
