In last year's presidential election, exit polls showed Obama trounced GOP nominee Mitt Romney among Hispanic voters.
"The fact that immigration reform looks possible is significant," Avlon said, saying passage of a bill would be a "significant legacy accomplishment" for Obama and also a boost for Congress at a time of extremely low public approval ratings.
Republicans led by Sen. Jeff Sessions of Alabama consider the immigration measure drafted by a bipartisan Senate "Gang of Eight" little more than amnesty for undocumented immigrants. They demand stricter border enforcement provisions before providing legal status of the estimated 11 million immigrants in the country illegally.
Meanwhile, the Obama administration is looking at possible options this week to increase support to Syrian rebels after resisting persistent calls for months to provide weapons.
"There is a recognition that unless we provide help, a lot of help, the situation is going to be very, very terrible," one senior administration official said.
The official described a "somber mood" among Syria hands throughout the administration, who remain frustrated at inaction by the Obama administration in the face of a deterioration on the ground in Syria and spillover to neighboring states like Lebanon.
GOP scrutinizes Justice Department
Republicans are quick to seize on any foreign policy objection with the Obama administration as an opening to attack former Secretary of State Hillary Clinton, who is considered the leading possible Democratic presidential contender in 2016.
In the House, the Oversight and Government Reform Committee has demanded more information on erroneous talking points by the administration four days after the terrorist attack last September on a diplomatic outpost in Benghazi, Libya, that killed four Americans, including Ambassador Christopher Stevens.
Rep. Darrell Issa of California, the panel's GOP chairman, also is a leading critic of Attorney General Eric Holder over the botched "Fast and Furious" gun walking program and other issues.
Holder now faces further scrutiny over the Justice Department's secret subpoenas of phone records for Associated Press journalists last year as part of an investigation of a classified leak.
He has told legislators he recused himself from that case and never would prosecute a journalist for doing investigative reporting.
Republicans question if Holder lied to Congress when he told a congressional hearing last month that he had no knowledge of any possible prosecution of journalists linked to classified leaks.
Avlon said the various issues provide grist for Obama critics now, but the major factor in determining public opinion on a presidency will be the economy, which is moving in the right direction for the White House.
"Teflon presidents are Teflon in part because of the economy," he said, rejecting accusations by some conservatives that Obama's troubles amount to scandals that could lead to impeachment.
"The impulse to simply throw out Nixon narratives as a poster boy for the second-term curse is silly," Avlon added. "This ain't Watergate and calls for impeachment reflect hyperpartisan wishes rather than reality."