In his weekly radio address, Mr. Bush said the deal fell apart when Minority Leader Harry Reid refused to permit votes on more than three Republican-backed amendments.
"I call on the Senate Minority Leader to end his blocking tactics and allow the Senate to do its work and pass a fair, effective immigration reform bill," the president said.
Reid shot back that Bush and Frist "are flat-out wrong about what happened to the immigration bill," saying Democrats proved their commitment to a comprehensive, bipartisan measure by voting twice in favor of it.
"It was President Bush and Republicans in Congress who lacked the backbone to stand up to the extreme right wing of their party, filibustered reform twice in two days, and put partisan politics ahead of border security and immigration reform," Reid said.
The deal had been hailed as a bipartisana day before it fell victim to internal disputes in both parties.
The measure offered eventual citizenship to millions of illegal immigrants. It would have strengthened border security, regulated the future entry of foreign workers, and created a complex new set of regulations for those in the U.S. illegally.
Theamid partisan bickering over adding amendments to the legislation. The bill managed only 38 votes on a key procedural test, far short of the 60 needed to advance. But what appeared to be a messy spat over process turned out to be a nasty political brawl, CBS News correspondent Gloria Borger reported.
Reid said on Friday, "The amendments were being offered by people who didn't want the bill."
Senate Democrats blamed Republicans for insisting on amendments that would weaken a compromise that Senate leaders in both parties had.
Senators say they'll come back after the two-week spring break and try again, reported CBS News correspondent Bob Fuss.
But, as members of Congress return home for their spring break, the first things many will see — from Los Angeles to the nation's capital — are thousands of immigration protestors, Borger reported. Massive demonstrations in support of a path to citizenship for the 11 million illegal immigrants now in the country are planned for Monday.