They questioned whether it had an effective strategy for raising the skills of the workforce, and urged it to get more business people, especially from small companies, involved in its work.
Last week Education Secretary Charles Clarke said the future of the economy depended on boosting skills of workers, and the burden of achieving that fell on the LSC.
If it looked like it was failing Mr Clarke would take the "Armageddon" option and use his powers to direct and control.
Barry Sheerman, chair of the education select committee, asked why there had been a skills task force, a workforce development strategy, and now a new government national skills strategy.
"Why do we need three goes at this? Are you blundering about in the dark because you have no idea of where you are going, because you have no strategy?" he asked Bryan Sanderson chair of the LSC.
Mr Sanderson said the council had been given the challenging task of trying to turn round about 100 years of neglect. This could not be done in one year.
The council expected to exceed its basic skills target and it had an ambitious Modern Apprenticeship MA programme.
It had sent a mailshot to employers to encourage their involvement with MAs. But it barely had "radar contact" with many small business people, whose first concern was to make money. They were not ready to give up their time to serve on local councils. Mr Sheerman said the LSC should be banging on Mr Clarke's door to get payment for them.
He also expressed a "voice of concern" about the pattern of mergers between higher and further education. He was worried that genuine FE would lose its focus.
Mr Sanderson said that in business 60-70 per cent of mergers failed. "The one that suffers is the one with the lowest esteem. We have to be very careful about that."
The LSC is to make a 10 per cent cut in its staff, around 500 people, and reduce bureaucracy. It aimed to increase productivity by 66 per cent by 2006