Ken Livingstone, Labour MP, in the latest edition of the left-wing paper Tribune, described the Bill as a "learning tax which is going to deter hundreds of thousands of potential students, and will not even resolve the long-term problems of higher education funding".
He predicted rebellion, saying a poll of Labour MPs last September showed less than half supported tuition fees. A spokeswoman from the National Union of Teachers said: "The rocky ride in the Lords augurs well. We know of at least 40 MPs who support our opposition."
Peers supported a Tory amendment which guaranteed poor students up to half of their maintenance costs. And an amendment to ensure English students pay the same as Scots taking four-year degrees in Scottish universities was also passed.
The Government said it will reverse the two Lords defeats.
The Teaching and Higher Education Bill introduces means-tested annual tuition fees of pound;1,000 and a new student loans scheme. Maintenance grants will be recouped via contributions to the Inland Revenue once a graduate is earning pound;10,000.
It could be argued that Baroness Blackstone, higher education minister, got off lightly. The earlier stages of the Bill saw peers apoplectic over its lack of detail and threat to academic freedom. In the event, Tories and Lib Dems found themselves attacking it from different and irreconcilable flanks.
The Tories supported the tuition fees, but were against the replacement of maintenance grants with loans. The Liberal Democrats are against the tuition fees, but support loans for maintenance grants. A Lib-Dem amendment that would have nullified fees was defeated by 14 votes.
Lord Glenamara, the former Labour education minister Ted Short, opposed the Government. He said he had been to college on a loan and had lived in poverty for many years attempting to pay it off.
Lady Blackstone said that by 2015 to 2016 the extra money from fees will amount to between pound;450 million to pound;500m - and pound;550m to pound;600m from the switch from loans to grants.
At next week's third reading, the Liberal Democrats hope to return to tuition fees. The Government did agree that tuition fees would not be increased beyond inflation, but peers will call for an independent committee to review student finance changes.
The Bill also establishes a general teaching council. At an earlier report session, Lady Blackstone said she would agree to the majority of council members being serving teachers. She would consider the inclusion of newly-retired teachers and commit the Government to consult the Churches and parents being represented.
An amendment to allow the GTC to remove members from its list - thereby barring them from the profession - was resisted by Government. Crossbencher Lord Baldwin said the council would be a "toothless creature" without the power, and, though he withdrew the amendment, said he would bring back at the next week with modifications.
A mandatory qualification for heads and a probationary year for new teachers met with cross-party agreement.
The Government, responding to peers' concerns, added amendments giving the Office for Standards in Education the power to inspect teacher-training institutions. These would restrict the chief inspector's brief to teacher-training courses and require him to give eight weeks written notice.