Washington (CNN) Hill lawmakers on both sides of the aisle had a similar reaction to President Donald Trump's talk of a grand immigration reform compromise: We'll believe that when we see it.

Despite wide support in Washington for a lofty ideal of someday reaching a bipartisan compromise on immigration, heavy skepticism remained Wednesday that Trump would be able to achieve such a feat, despite his remarks on Tuesday that he hopes to do so.

Many of the same sticking points remain that have always plagued immigration reform.

On the right, Republicans want to see enforcement of immigration laws beefed up first, achieving border security before addressing the estimated 11 million people already living in the US illegally. GOP lawmakers also have concerns about the cost of some of Trump's proposals, including a wall along the entire Southern border, which some Republicans doubt is necessary.

On the left, Democrats don't believe Republicans are serious about being sympathetic to non-criminal undocumented immigrants, some of whom contribute to their communities and have lived in the US for years without legal status. They also point to Trump's rhetoric and actions on immigration as a non-starter.

Ultimately, lawmakers from both parties say they're waiting for more show than tell from Trump on what he actually wants.

"As was the case with much of the speech, the blanks weren't filled in, so I think at the end of the day on an issue as big immigration, an issue as big as tax reform, it's going to require presidential leadership," said South Carolina Republican Rep. Mark Sanford, a conservative who has been unafraid to criticize Trump.

"It was not found in the joint address -- but it's going to be needed," Sanford continued.

Trump on Tuesday sent mixed messages to lawmakers on his immigration plans. In a meeting with reporters at the White House, Trump signaled he'd be open to a grand compromise, and a senior administration official said that would include a path to legalization for undocumented immigrants living in the US.

"The time is right for an immigration bill as long as there is compromise on both sides," Trump said.

He followed that meeting up with his joint address to Congress -- where he did not advocate legalization but said that he still thinks meaningful immigration reform could be achieved.

"I believe that real and positive immigration reform is possible, as long as we focus on the following goals: to improve jobs and wages for Americans, to strengthen our nation's security and to restore respect for our laws," Trump told lawmakers.

But during the speech, he also reiterated his campaign pledge to build a "great wall" on the border, and welcomed guests who were victims of crimes allegedly committed by undocumented immigrants to announce a new victim's office at the Department of Homeland Security. Trump's speech also focused on the criminals and terrorists he sees among immigrants

Democrats said Wednesday that Trump's supposed olive branch was nothing of the sort.

"It was one brief mention," said California Sen. Dianne Feinstein, the top Democrat on the Judiciary Committee. "I had expected more because we had all read the press that he was going to move to a broader program, both for DACA and others who are here in undocumented capacity. And all that was said was merit-based."

However, Feinstein said she would welcome if Trump were serious about a pathway to legal status for undocumented immigrants.

Senate Minority Leader Chuck Schumer implied the President played the media to indicate he was open to immigration reform, only to deliver a different message in person.

"It was so funny, he spoke to a bunch of cosmopolitan news anchors and mentioned maybe he will change his views on immigration and the media got into a buzz about that," Schumer said on the Senate floor Wednesday. "The speech he gave was one of the most anti-immigrant speeches that we heard any president ever give -- saying one thing, doing another. "

Arizona Democratic Rep. Ruben Gallego, a vice chair on the Congressional Hispanic Caucus, threw cold water on the idea that Trump could be using his hard-line immigration posture in search of reform.

"This is not Nixon goes to China," Gallego told CNN. "One, he's not that bright, and two, not that committed. He's going to fumble it in one manner or another, and at the end of the day, as soon as he feels pressure from the right, he'll fold."

Like Sanford, Republicans expressed a range of doubts about the President's proposals.

Senate Judiciary Chairman Chuck Grassley said establishing border security would be a necessary first step, and that he wouldn't discuss legal status before that was achieved.

"Before you even deal with that question, you've got to take care of these other things," Grassley said. "That's the most important thing you've got to build confidence for."

Republican immigration hawk Texas Sen. Ted Cruz wouldn't respond to media reports that the President was open to legalization, saying that he would wait to hear it from Trump himself -- but signaled opposition.

"My view is we need to secure the border, which is what ... President Trump talked about last night. We need to reform the legal immigration system. That's also what President Trump talked about," Cruz said. "I don't support amnesty, but I'm not going to chase ghosts ... I'm going to wait until we see specific legislative proposals."

Oklahoma Sen. James Lankford said the wall had to be paid for, and Sanford echoed that concern. Ohio Sen. Rob Portman, a moderate, also questioned the efficacy of a wall.

"There are parts of the border where an actual wall would be incredibly expensive for taxpayers and incredibly expensive to monitor," Portman said. "I think there's a way to do this, but not on the entire border."

Meanwhile, conservative hard-liners said they heard no shift in Trump's tone on immigration, despite the earlier comments to reporters.

"People heard other things, (but) I always heard Trump saying let's make Americans feel safe first and then deal with all these other issues," Idaho Rep. Raul Labrador said. "That's what I heard last night and I have heard that from the moment he talked about immigration."

Echoed Arizona Rep. Trent Franks:

"I heard last night on the news that there was a major shift -- I have not heard anything from him yesterday or today that indicates any similitude to that, anything that I can find consistent with that," Franks said. "If that has happened, it is absolutely without my knowledge."