US Senate leaders are battling to hold together a fragile compromise on an overhaul of the immigration system.
The bill would tie tough border security and workplace enforcement measures to a guest-worker programme, but the plan to legalise the millions of illegal immigrants is under attack from the right and left.
The bill has been supported by the Irish lobby seeking the regularisation of around 25,000 undocumented Irish.
Conservatives argue it will give amnesty to people who broke US laws, while unions say the temporary worker programme will create an underclass of cheap labourers.
President Bush defended the bill as a comprehensive approach that will fix what most Americans believe is a broken immigration system through which millions of illegal immigrants have entered the United States.
"If anybody advocates trying to dig out 12 million people who have been in our society for a while, you know, it's sending a signal to the American people that's just not real," Mr Bush said.
A New York Times/CBS News poll showed a large majority of Americans in favour of changing immigration laws to allow illegal immigrants to gain legal status and to create a guest-worker programme.
So far, the handful of leading senators who helped broker the compromise with the White House have fended off amendments that would have crippled the delicate compromise.