Democratic leaders used a Capitol Hill rally Wednesday to continue pushing the Senate to take a piecemeal approach to President Barack Obama’s jobs bill, even as the chamber struggled to finish work on a package of three spending bills.

“We are going to make sure there is a vote on our bill this week,” Senate Majority Leader Harry Reid said, referring to a $35 billion measure for states and localities to retain teachers and first responders that the Nevada Democrat wants to add to the minibus appropriations measure. “And to make sure that we do that, I will protect [myself] by filing cloture unless we can work something out.”

The aid measure is the first portion of Obama’s $447 billion jobs bill that Reid wants the Senate to take up.

But it is not expected to win the 60 votes needed to overcome a filibuster and not even all 53 Democrats are expected to back it. The bill would be paid for with a 0.5 percent tax on millionaires, which Republicans have called a populist ploy and not serious policy.

Reid blamed Republicans for obstructing the Democrats’ agenda and rooting for the economy to fail in order to hurt Obama’s re-election prospects.

They want to do “whatever they can do to make Barack Obama’s life miserable,” Reid said.

The rally was also attended by Vice President Joseph Biden, who asked voters to push Republicans to work with Democrats and vote for the teachers bill.

“This wasn’t designed to put any Republicans on the spot,” Biden said, adding that many Republicans have supported pieces of the jobs bill previously.

Biden’s comments come after the overall $447 billion jobs bill fell to a filibuster last week. His comments also come as Obama is wrapping up a bus tour touting his jobs plan in North Carolina and Virginia.

Now, “we are going to take up this legislation piece by piece,” Biden said.

But Republicans see the move as nakedly political — an effort to help Democrats in their re-election campaigns, including the president’s.

“The president proposes a stimulus bill, which he calls a jobs bill,” Senate Minority Leader Mitch McConnell (R-Ky.) said Wednesday on the floor. “Congress rejects it in a bipartisan way for very sensible and straightforward reasons.

“The president then goes on a bus tour to criticize Republicans for voting against this so-called jobs bill,” McConnell continued. “Democrat leaders consult with the White House on breaking the same bill into smaller pieces … identifying parts they know Republicans will oppose and adding on a tax hike just to make sure.

“Repeat for 13 months [until the 2012 election] in the hopes that Americans will forget that they’re all now living under the economic policies that were enacted during the first two years of the Obama administration,” McConnell said. “In other words, they’re actually designing legislation to fail over on the other side, so they’ll have someone else to blame for the economy 13 months from now. That’s what’s going on in the Senate this week.”

Despite the partisan asides, the Senate did make some progress on the spending package, which is made up of the Commerce, Justice and science; Agriculture, rural development, and Food and Drug Administration; and Transportation and Housing and Urban Development appropriations measures.

“Hopefully, we’ll finish” with the appropriations bills so that the chamber can take up the teacher and first responder package, Sen. Charles Schumer (N.Y.) said after addressing the rally. Schumer heads the Senate Democrats’ policy and communications operations.

The Senate continued to plow through amendments into Wednesday evening. Earlier in the day, the chamber rebuffed an effort by Sen. John McCain to include language in the spending package that would prohibit funding for low-priority transportation projects such as historic renovation and beautification.

The Arizona Republican argued that the requirement has led to a series of questionable projects such as white squirrel sanctuaries, a national Corvette museum simulator theater and bicycle museums.

“One of my favorites is a roadside museum featuring a giant coffee pot,” he said.

McCain said it is galling that highway funding is used for such projects when roads and bridges remain underfunded.

“Its also a fact that more people travel over deficient bridges every day … than go to McDonald’s,” McCain said. “We have to set priorities, and I would like the states to set those priorities rather than have it be mandated.”

Sen. Patty Murray (D-Wash.), chairwoman of the Appropriations Subcommittee on Transportation and Housing and Urban Development, and Related Agencies, who opposed the amendment, said the measure would go too far by prohibiting any landscaping and preservation activities by HUD and the Transportation Department, including the use of Community Block Development Grant funds for historic preservation, basic landscaping and streetscaping activities.

She said the amendment also would “cripple Amtrak,” which has to maintain 126 stations in 41 states “that are on the national register of historic places.”

The chamber voted to table McCain’s amendment, 59-39.