President Barack Obama on Tuesday showed once again that he is willing to bet against the odds by trying to appeal to Congress to take on climate change and comprehensive immigration reform — two issues that have otherwise fallen off the calendar for the year.

Obama met for more than an hour and a half with a bipartisan group of Senators to build support for passing an energy bill this year. Later Tuesday, he sat down with a completely different group of lawmakers — nearly two dozen members of the Congressional Hispanic Caucus — to discuss immigration reform and what kind of package stands the best chance of passing into law.

Neither issue currently has the bipartisan support it needs to advance. And with many House Democrats wary of taking tough votes in the lead-up to November elections, the likelihood of either becoming law this year is slim.

But that isn’t stopping Obama from trying to change minds on Capitol Hill. And on at least one of those fronts, he appears to be making some headway.

Sens. Joe Lieberman (ID-Conn.) and John Kerry (D-Mass.), co-sponsors of comprehensive energy legislation, emerged from their White House meeting citing “a breakthrough” in negotiations: A number of Republicans said they would be open to a pared-back version of a cap-and-trade bill, which so far has drawn no GOP support. Lieberman chalked up Republicans’ change of heart in part to Obama delivering a “very passionate” argument in favor of a carbon tax.

“Some of our colleagues who up until this time have been at least publicly reluctant about … putting a price on carbon pollution said they would be willing to discuss limited forms of doing that in this bill,” Lieberman said.

The Connecticut Senator said he is “not naive about the difficulty in an election year” of trying to move a sweeping energy bill, but after meeting with Obama, he said he feels more “optimistic and encouraged … that we can make something very good happen.”

Kerry said he will be pressing to have a bipartisan proposal on the table in early July and is prepared to scale back his measure to bring some Republicans on board. He said he already has a commitment from Sen. Olympia Snowe (R-Maine), and others, to work on a compromise blueprint together.

Senate Democrats have an ally in Snowe’s home-state counterpart, Sen. Susan Collins (R), as well. Collins said the meeting with Obama “went very well” and agreed with him “that there should be a clean energy component that puts a price on carbon.”

Sen. Judd Gregg also suggested that some in his party may be willing to compromise on the issue.

There was “more common ground than disagreement” in the meeting, the New Hampshire Republican said. “There is the opportunity to do an energy bill here.”

Other Republicans, including Sens. Lamar Alexander (Tenn.) and Lisa Murkowski (Alaska), left the meeting firmly opposed to any version of cap-and-trade legislation.

“Americans are focused on jobs,” Murkowski said. “That is the reason that a cap-and-trade proposal, a national energy tax, will not sell in this country at this time.”

Meanwhile, Obama is giving yet another push to move immigration reform. Latinos have been pressing Obama to keep the issue alive, even though Republicans and some Democrats have balked at the idea of taking on such a toxic issue in an election year.

Afterward, Rep. Luis Gutierrez (D-Ill.) said, “There is no good reason why we cannot have comprehensive immigration reform this year if a handful of Republicans put solving problems ahead of playing politics.”

In addition to Tuesday’s meeting with Hispanic lawmakers, Obama sat down with grass-roots immigration activists Monday and told them that he is pressing for action based on a proposal floated by Sens. Charles Schumer (D-N.Y.) and Lindsey Graham (R-S.C.). On Thursday, the president will also give a speech on the need for immigration reform at American University’s School of International Service.

“The president was very clear that he will work with us to frame the immigration issue for the American people in a new and aggressive way and he will start with his speech on Thursday,” Gutierrez said.

White House Press Secretary Robert Gibbs said Tuesday that Obama wasn’t going to announce any new developments on the issue and that his speech would “largely” be a reiteration of what he keeps saying: that immigration reform “continues to be a very important national issue” and that it must done “in a comprehensive way.”

Gibbs said Obama will also emphasize that “he cannot do this alone” and will reach out to Republican Senators who previously worked on immigration reform legislation.

But at least one CHC member said the president and House Democratic leaders should press ahead with legislation now instead of waiting for GOP lawmakers to get on board.

“Some of us have been urging the fact that we need to start the legislative process. The White House and Congressional leadership Democrats need to be on the right side supporting this instead of sitting on our hands waiting for a Republican to miraculously appear. I think that’s part of the frustration, that there’s no movement,” Rep. Raúl Grijalva (D-Ariz.) said.

Grijalva added, before heading into the meeting with Obama on Tuesday: “Hopefully this is about creating some movement.”

Kathleen Hunter contributed to this report.