"The Rule... deems that the Republican (Ryan) Budget Resolution, which seeks to end Medicare, has passed both the House and the Senate," said an email from House Minority Whip Steny Hoyer (D-Md.). "The Rule deems that the Republican Budget, and all of its committee allocations, has been passed by both the House and the Senate for budget enforcement purposes, even though the Senate resoundingly rejected the Republican Budget. Members are urged to VOTE NO."

Republicans anticipated that Democrats would object to the rule, but argued that the only alternatives are to not begin work on the 12 annual appropriations bills, or somehow convince the Senate to begin negotiating with the House on a FY 2012 budget resolution. The Senate has so given no sign that it is prepared to take up any budget bill.

While Democrats were focusing on the budget language in the rule, House Republicans on Wednesday touted the fact that the rule for the DHS bill is the first open rule in nearly four years. Once passed, the open rule will allow members to offer a broad range of germane amendments to the bill.

House Rules Committee Chairman David Dreier (R-Calif.) indicated that House Republicans would allow the use of open rules for all appropriations bills as a way to help curb spending.

"As we work to get our fiscal house in order, it's absolutely critical that the House have the ability to closely examine every aspect of spending bills," Dreier said. "This open rule will allow us to do that."

Dreier added that past restrictions on amendments "correlated directly to the dramatic increase in spending over the last four years," and said it's time to reverse that trend.

Under the rule, the bill will be read in order, and members will be allowed to propose amendments to sections as they are read. Priority will be given to amendments that are pre-printed in the Congressional Record. The process is expected to start Wednesday with consideration and passage of the rule, and continue into Thursday as the bill and amendments are debated. Roll call votes on some amendments could take place Wednesday evening.

On the bill itself, Hoyer's office noted that it would cut DHS appropriations by nearly three percent from FY 2011 levels, is seven percent below the Obama administration's request, and would cut grant funding to state and local first responders by 60 percent. But Hoyer's note did not recommend voting against the bill.

-- This story was updated at 10:54 a.m.