House Majority Leader Steny Hoyer (D-Md.) said Tuesday afternoon that it was still unclear when the House would take a second crack at the bailout bill, but said bipartisan conversations were under way.

“I have already spoken with administration officials, as well as Congressional Republican and Democratic leaders about what needs to be done moving forward, and I will continue those conversations today,” Hoyer said in a statement.

“At this time, the House is scheduled to meet at noon on Thursday. It still remains to be decided when the House will consider new legislation regarding the economic crisis.”

Some Democrats are already putting forward alternative plans.

Rep. Peter DeFazio (D-Ore.), along with a handful of lawmakers who opposed the bailout, unveiled their proposal to direct the administration to take five steps to respond to the Wall Street meltdown. These include changing “mark-to-market” accounting rules, including stronger foreclosure protections and creating an emergency financial crimes office in the Justice Department.

House leaders were in a “needless rush” over the last two weeks and pushed lawmakers to act “in a way that we could not be deliberative,” said Rep. Marcy Kaptur (D-Ohio). “That is truly unfortunate.”

The ideas being put forward today are “much more market-oriented” and bring the “good Midwestern values of prudence and responsibility back to the markets,” Kaptur said.

DeFazio praised the idea of increasing Federal Deposit Insurance Corp. insurance limits and noted that there has been “some coming together” on this proposal. But he warned that it will take more than the Senate adding this provision to the current bailout bill to win more House support.

“If the Senate intends to jam through the same bill only with a change in the FDIC limit tomorrow night, if they do that without a real pay-for, I think there’s going to be tremendous problems in the House,” DeFazio said.