Senate Minority Whip Jon Kyl (R-Ariz.) indicated Tuesday that he does not believe his party can stop the package of fixes to the healthcare overhaul from passing the Senate.

The Arizona senator told CNN that he thinks in "roughly a week" President Barack Obama will sign the reconciliation bill that makes corrections to the legislation he signed Tuesday morning.

"I'm assuming that this bill eventually goes to the president, maybe in roughly a week or so," he said in an interview.

Senate Republicans plan to offer a host of amendments and points of order to the reconciliation bill this week, but Kyl's comments indicate that the Senate GOP's efforts can only slow the bill, not stop it entirely. 

Under the reconciliation rules, which Senate Democrats are using to sidestep a Republican filibuster and approve the fixes with a simple majority vote, senators can offer an unlimited amount of amendment after 20 hours of debate.

Sens. John McCain (R-Ariz.) and Tom Coburn (R-Okla.) rolled out several amendments earlier Tuesday and more are likely to come.

Kyl said that he hopes the amendments pass, which would force the House to take a second vote on the reconciliation bill they passed Sunday, but expressed doubt that enough Democrats would support them.

"And, you know, unless Democrats suddenly decide to accept some Republican ideas, chances are the bill is not going to be amended," he said. "Now, there could be points of order that lie against the bill. If so, we will sustain those and then the House would have to vote for the bill again."

Other Republicans have began efforts to knock down the new law. Bills have been introduced in the House and Senate that would repeal the legislation and 13 states that have Republican attorneys general filed a federal lawsuit Tuesday saying that the healthcare overhaul is unconstitutional. 

"Eventually, we hope that the bill will be repealed and replaced with other solutions to the problems that we all agree exist," Kyl said.