Vincent Cable, former chief economist at Shell International and now Liberal Democrat shadow chancellor of the exchequer, is to table an early day motion in the House of Commons in support of the magazine's campaign. MPs in other parties have indicated they will support the motion.
Paul Goodman, a front-bench Tory MP and a member of the work and pensions select committee, said he would ask his party to back the motion.
Labour MP Brian White, who worked in the IT industry for 20 years and who sits on the public administration select committee, said he supported the campaign to improve accountability on public sector projects.
Yesterday, MPs on the Commons work and pensions subcommittee took oral evidence from specialists, including Computer Weekly, on how the delivery of government IT projects could be improved.
Computer Weekly's campaign has two main objectives. It seeks to persuade the government to publish Gateway reviews in which specialists employed by the Office of Government Commerce assess a project in its various stages.
Some reviews have helped to reduce the risk of failure, but others have endorsed projects, including those that supported the introduction of tax credits and the checking of criminal records, which went live with damaging consequences.
Publishing Gateway reviews would introduce a level of accountability for ministers and departmental heads that currently does not exist. It could also, for example, show that IT executives in a department had warned of the risks associated with a project, or had sought more time for testing, but had been overruled.
Computer Weekly is also campaigning for legislation that builds on the most successful aspects of specific IT laws in the US.
In a statement on Computer Weekly's campaign, Cable said last week, "I will be tabling an early day motion to call on the government to take action to avoid IT disasters. We will be calling for the publication of Gateway reviews and legislation to enshrine best practices."
An early day motion is a means by which MPs can put on record their opinion on a subject and canvass support for it from other members.
White, who has worked in the public and private sectors, said there were probably more project failures in commercial operations. But he added that there was a lack of accountability in both sectors. "Shareholders are kept in the dark about projects that fail," he said.
Meanwhile, Computer Weekly readers have expressed strong views on the causes of IT failures in government. Many think the problems are deep-rooted.
MP Richard Bacon, a member of the House of Commons Public Accounts Committee, said, "IT professionals should urge their MPs to get behind this campaign. We have volumes of best practice guidance and numerous codes of conduct but there is no let up in the number of project failures. Openness and accountability are key steps on the road to putting things right."