Sen. Bob Corker is saying openly what other Republicans seem to be thinking behind the scenes: The strategy to defund Obamacare is raising expectations among conservatives to unrealistic levels.

“It seems to me that the House sends over a piece of legislation, we are easily going to support it. We are also going to probably support ending debate,” the Tennessee Republican said, adding that under Senate rules, Democrats would have a chance to amend the bill post-cloture to eliminate the language defunding Obamacare.

“It just seems to me that what’s happened unfortunately is that American expectations on Republicans and what they can do have been raised to a level that’s beyond delivery,” Corker added.

Corker’s comments came after he took what some might construe as a swipe against Sen. Ted Cruz, R-Texas, on Twitter earlier in the day.

I didn’t go to Harvard or Princeton, but I can count — the defunding box canyon is a tactic that will fail and weaken our position. –BC

— Senator Bob Corker (@SenBobCorker) September 19, 2013

Sen. Charles E. Schumer, the No. 3 Democratic leader, told reporters that one of the problems with the Cruz-backed effort is that supporters don’t seem to know the outcome.

“They have this hard-nosed, adamant, almost surreal tea party saying go ahead and do it, and the tea party doesn’t even know how it’s going to end,” the New York Democat said.

Without referring to anyone by name, Senate Majority Leader Harry Reid likewise said that the defund Obamacare advocates are really seeking publicity.

“These are not just games to the middle class in America. While Republicans in Washington use these stunts to raise money and grab headlines, people in Nevada and around the country are going to feel the pain of this economic shutdown,” Reid said. “The consequences of shutdown are deadly serious.”

“I will do everything necessary and anything possible to defund Obamacare,” Cruz said at a news conference with House conservatives, adding that in addition to a classic filibuster, he would use “any procedural means necessary.”

“Listen, this is the most important fight in the country, and it’s easy to focus on the political back-and-forth,” Cruz said. “This is going to be an iterative process. In all likelihood, it’s not going to be a single-shot CR and everything’s resolved.

Cruz continued: “If and when we win this fight, it is going to be because House Republicans have stood up and showed the courage that they are showing right now, that they continue to stand up. The House is the one branch of government that Republicans have a majority.”

Asked about the suggestion by Cruz that GOP House members should reinsert language to defund Obamacare if Reid strikes it out of the bill, Sen. Mike Johanns, R-Neb., demurred.

“I just avoid weighing in on telling House members how they should run their world over there,” Johanns said. “From my vantage point on the Senate side, it was always clear to me under the rules here at the Senate, you know, the majority leader has that kind of power. I couldn’t see how we would end up voting for this.”

Johanns said he’d look at the whole bill before deciding how to vote on a debate-limiting cloture vote, which would likely come while the bill still has Obamacare defunding language. A number of Senate Republicans are likely to oppose that vote based on the spending level in the bill, rather than the Obamacare issue that’s getting so many headlines.

Seven Senate Republicans, led by Jeff Flake of Arizona, sent Reid a letter Thursday calling for a continuing resolution at a $967 billion spending level, which is the sequester level for fiscal 2014. That’s as opposed to the roughly $986 billion level in the House CR.

“While potentially politically expedient in the short term, it is difficult to conceive of a fiscal test by which the consideration of spending legislation for next year authorizing a funding level higher than $967 billion could be viewed as responsible,” the letter said.

White House spokesman Jay Carney signaled Thursday that President Barack Obama would accept a stopgap spending measure at the House level (with Obamacare funded, of course).

“The president has been and is willing to negotiate with Republicans over a broad compromise on budget, on funding and spending,” Carney said. “He has put forward his own proposal to do that, and he urges Congress to act to make sure the government does not shut down and continues to be funded, and if necessary, to pass a short-term extension of funding at current levels in order to allow for further negotiations on a broader budget agreement.”

 Steven T. Dennis contributed to this report.