Senate Minority Leader Mitch McConnell (R-Ky.) said Friday he is still trying to convince Sen. Jim DeMint (R-S.C.) to drop his objection to sending a lobbying and ethics bill to conference with the House, while acknowledging that Senate Democrats may instead have to use an end-run tactic to get the bill to the president’s desk.

When asked whether he could convince DeMint to stop standing in the way of the conference committee, McConnell responded, “We’re trying.”

At a press conference earlier, McConnell said he would like to send the legislation to conference to ensure that Republicans can participate in negotiations over the final bill, but he said the measure’s importance and DeMint’s continued intransigence may outweigh his preference.

“Without a conference, the minority won’t have any impact on the outcome of the bill,” said McConnell. He added, “So, from a leadership point of view, my preference would be to go to conference. There’s at least one member of my group that doesn’t share that view. … Either way, I think we ought to wrap the bill up.”

McConnell co-sponsored the measure along with Senate Majority Leader Harry Reid (D-Nev.), and it was the first bill the Senate passed this year. But DeMint has repeatedly objected to sending the bill to conference until the Senate adopts strict rules on earmarks that passed as part of the bill. Democrats have acknowledged they might want to alter those rules in conference.

Reid said Friday he was planning to use a maneuver — which the House and Senate employed on the second version of this year’s Iraq War spending bill — that would bar amendments and only require one cloture motion, or motion to limit debate.

Typically, Senators have the ability to force multiple cloture motions on bills. Under the likely process for the lobbying and ethics bill, the House will amend the Senate bill and then send it to the Senate for concurrence. Reid can use a procedure called “filling the amendment tree” to prevent any further Senate amendments.

The House will “send us a message, and we’ll accept or reject the message. I’ll have to file cloture on it, but only once,” Reid said.

A House leadership aide said Friday that the House and Senate were still negotiating the details of the legislation so the two chambers could approve identical bills to send to the president. In particular, language regarding new disclosure requirements for lobbyists who bundle campaign contributions remained unresolved.

Both bills contain bundling language that requires lobbyists to disclose how much and who they are bundling cash for, but the House bill includes broader reforms, including a requirement for lobbyists to certify via mail to the recipient of the contributions exactly what will be reported.

If House and Senate leaders can work out the details, the bill could be on the floor as early as this week. Aides in both chambers said it is a top priority for Reid and Speaker Nancy Pelosi (D-Calif.) to complete the bill before the August break. Reid has threatened to hold up the recess if the lobbying and ethics reform bill is not done. Pelosi has not made a similar threat at this point.

Meanwhile, Reid and McConnell also said they hope to complete the conference on a bill to implement the terrorism-prevention recommendations of the 9/11 commission before Congress recesses.

Because Democrats agreed to remove provisions related to collective bargaining for airport screeners, McConnell said he hopes the president will sign the bill, but he criticized Reid for only scheduling debate on one appropriations bill this month.

“They were highly critical of us — and we deserved the criticism — for not getting our appropriations bills done last year,” said McConnell. “This is the basic work of government. We haven’t even started.”

But once appropriations bills do come to the floor, McConnell said Reid could expect “substantial bipartisan cooperation,” and he predicted a relatively smooth Senate floor debate this week on the Homeland Security spending bill.