Senate Majority Leader Harry Reid (D-Nev.) put Republicans on notice Thursday that Democrats have no intention of abandoning their healthcare reform efforts.

Reid, in a letter to Minority Leader Mitch McConell (R-Ky.), said Democrats have every intent to "finish the job" on healthcare.

"Many Republicans now are demanding that we simply ignore the progress we’ve made, the extensive debate and negotiations we’ve held, the amendments we’ve added (including more than 100 from Republicans) and the votes of a supermajority in favor of a bill whose contents the American people unambiguously support.," Reid said. "We will not. We will finish the job."

The letter comes as Democrats in the House and Senate work to wrap up their months-long health reform effort, eyeing the budget reconciliation process to do so. The plans under consideration would have the House pass the Senate bill, and then begin new legislation to make fixes to the original legislation. Those changes would be passed through the reconciliation process, which lets senators pass a bill with a simple majority of votes, instead of the 60 normally needed to end a filibuster.

Republicans have decried the process as hyperpartisan and unprecedented on a piece of legislation of this scale. They've also vowed to raise points of order, and throw up other roadblocks to the reconciliation package, which would effectively conclude the healthcare debate.

Reid defended the process in his letter to McConnell as an attempt to make only a few changes to the much larger package, which has already passed the Senate with 60 votes.

"Reconciliation would be used to make a modest number of changes to the original legislation, all of which would be budget-related," the majority leader said. "There is nothing inappropriate about this."

But Reid left open the door to Republican participation in the Senate debate, while implicitly warning against any GOP attempt to prevent an up-or-down vote on the legislation.

"Keep in mind that reconciliation will not exclude Republicans from the legislative process. You will continue to have an opportunity to offer amendments and change the shape of the legislation," Reid wrote. "In addition, at the end of the process, the bill can pass only if it wins a democratic, up-or-down majority vote.  If Republicans want to vote against a bill that reduces health care costs, fills the prescription drug 'donut hole' for seniors and reduces the deficit, you will have every right to do so."