Mirroring the continuing decline in his popularity, a latest Newsweek poll indicated that half of Americans now wish to replace Bush in next year's elections.
A YouGov poll in the UK also underlined the declining fortunes of Blair.
While Blair's personal approval rating slid down to 37% from 40% just a week ago, the poll said the opposition Conservatives have now overtaken the ruling Labour.
For both Bush and Blair, the slide in ratings is worrisome.
With support of 38%, opposition Conservatives in UK were five points ahead of Labour's 33%.
Blair has reasons to be grim
The gap was also said to be closing in the US between the president and his prime challenger, with the Newsweek poll suggesting that Democrat presidential hopeful, Wesley Clark, was making rapid strides.
Clark was preferred by 43% of the registered voters, against 47% who opted for Bush.
Clark topped the list of Democratic challengers, followed by Joseph Lieberman with 13% support. The other hopefuls lay far behind.
Bush's weak spot, the economy, was a priority for 44% of those polled.
The president's handling of Iraq was disapproved by 49% of those polled. Only 44% approved the war.
The poll surveyed about 1004 adults over a two-day period this week.