The government has accepted there is a “real risk” its plans for a referendum on electoral change could be delayed by ongoing debate in the House of Lords.
But Lords leader Lord Strathclyde said he hoped to find a “sensible and constructive way forward”.
He added that ministers were willing to accept changes.
Labour’s Lord Falconer said he believed there could be “give and take”. Peers held all-night sittings last week amid bitter disputes over the plans.
The Parliamentary Voting System and Constituencies Bill would schedule a referendum on bringing in the alternative vote (AV) system for Westminster elections on 5 May.
It also contains provisions for the number of MPs to be cut from 650 to 600 and for constituency boundaries to be re-drawn.
Labour argue that these plans should be separated into two bills, but the coalition says they are part of the same overall package of reform.
Peers spent many hours discussing the proposals last week, with no obvious end in sight.
Under the AV system, voters rank candidates in their constituency in order of preference.
Anyone getting more than 50% of first-preference votes is elected.
If no-one gets 50% of votes, the candidate with the fewest votes is eliminated and their backers’ second choices allocated to those remaining.
This process continues until one candidate has at least 50% of all votes in that round.
Vote reform: Where parties stand Q&A: Alternative Vote referendum
The Electoral Commission needs a full 10 weeks, as set out in previous legislation, to fully prepare for a referendum, meaning the bill would have to receive Royal Assent by 16 February.
Government sources have indicated that, if no deal is reached, ministers may seek to force the measure through the Lords by a series of “guillotine” motions.
This would be unprecedented and likely to result in widespread opposition in the House of Lords, which traditionally is self-regulating when it comes to debates.
Lord Strathclyde told his fellow peers: “We are open to changes to this bill, but not the fundamental thrust of this bill…
“We must together find a way for the House to consider this bill in a timely manner.”
He added: “At some point we may need to review how well our conventions work, rooted as they are in the principle of self-regulation… I’m sure we can find a sensible and constructive way forward.”
For Labour, former Lord Chancellor Lord Falconer promised to respond “constructively” to the government’s comments.
He added: “I urge the government to redouble efforts to reach a compromise… We are at an impasse…
“The right of the government to get its bills passed in reasonable time has to be balanced by the right of the opposition to give reasonable scrutiny to a bill…
“We stand ready for positive discussions.”
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