The government's Lords reform proposals face a battle to be accepted after coming under fire on several fronts.
Lords reform plans face a rough ride
The Lib Dems gave them a guarded welcome but Lord Strathclyde, Tory leader in the Lords, said he would struggle to support the "botched" plan.
The reaction on the Labour benches was mixed, with some arguing the reforms could lead to political deadlock.
Mr Straw is seeking cross-party backing for a chamber made up of appointed and elected members.
A 'hybrid' of elected and appointed peers
Reduce size of House from 746 to 540 members
End hereditary and life peerages over time
Elected peers to be voted in at same time as Euro elections
Maximum time in office of 15 years for elected and appointed peers
Appointees a mixture of party politicians and non-party figures
Lords may be renamed - possibly 'The Reformed Chamber'
Anglican bishops and archbishops to keep seats
But he said he would consider using the Parliament Act to force the changes through if the Commons and Lords fail to reach an agreement on the way forward.
"Ultimately, it is for the Commons to decide what becomes law," he told BBC Radio 4's PM.
Under Mr Straw's proposals, members of the Upper House of Parliament will no longer be made peers and the House of Lords itself will change its name.
The chamber would be slimmed down to 540, including directly-elected members for the first time.
The 92 places for hereditary peers would be scrapped, but Mr Straw left open the question of whether those currently sitting in the Lords should be removed immediately - and, if so, whether they should be offered any compensation.
He has described the proposals as the "best opportunity" to reform the House of Lords for "many decades".
But he also stressed, during business questions in the Commons on Thursday, that the reforms were still at a very early stage and MPs would given an opportunity to debate changes.
He was responding to calls from backbench Labour MPs for a referendum on Lords reform and a vote by MPs on whether Bishops should continue to sit in the second chamber.
Mr Straw has said he personally favours 50% of members being elected, 30% being appointed from party political choices and 20% being appointed from among non-party candidates
Prime Minister Tony Blair, who has previously backed an all-appointed second chamber, has said he backs Mr Straw's strategy of seeking to find a consensus on a part-elected Lords.
However previous attempts to get MPs to agree on what proportion of the Lords should be elected have failed to get a majority for any particular figure.
Mr Straw's controversial plan to get round this is to give MPs seven options - ranging from all elected to all appointed - which they rank in order, with the last place one dropping out and its second choices reallocated, until one option has majority support.
But this preferential voting plan must first be agreed by Parliament, with Labour MPs forced to vote for it on a three line whip, angering the government's critics.
Conservative MP Sir Patrick Cormack, of the cross-party Campaign for an Effective Second Chamber, said: "What he [Jack Straw] has proposed today is a constitutional outrage.
"Will he give everybody on his side of the House a free vote on this monstrous proposal for a football-coupon ballot?"
The preferential voting system was also opposed by Labour backbenchers Gerald Kaufman and Alan Williams, but Mr Straw insisted it was necessary to avoid the "train wreck" of 2003 when Parliament voted to reject all options.
Chancellor Gordon Brown has yet to make his views known, but is reported in Thursday's Daily Mail and Guardian to support a wholly-elected Lords, if Mr Straw's proposals are blocked and he becomes prime minister.
Lord Strathclyde said Mr Straw would struggle to convince Conservatives his plans were "worth the paper they are written on".
He said the Conservatives had been expecting to see proposals "that we could sign up to, but instead there was a mish-mash of compromise, of appealing to the lowest common denominator".
Calling for 80% elected peers, Lord Strathclyde said: "I accept that that isn't going to happen for a very long time, but that is the principle that we should be aiming at."
Liberal Democrat constitutional affairs spokesman Simon Hughes said: "We welcome what is clearly a serious attempt by the government to complete the process of reform that began nearly 100 years ago.
"The Liberal Democrats have always been committed to a wholly or substantially elected second chamber."