With the Senate ready to cast the first floor votes on a landmark immigration bill, House Speaker John Boehner said Tuesday he thinks there’s a good chance the legislation can be signed into law “by the end of the year.”

Ahead of Tuesday afternoon’s procedural votes to officially allow debate to move forward, senators were readying amendments on contentious issues including border security, back taxes and health care coverage. Some Republicans said they were seeking to strengthen enforcement provisions so that they could be comfortable voting for the bill.

Other GOP measures were already being dismissed by Democrats as attempts to kill the bill by striking at the fragile compromises at its core.

Boehner said in a nationally broadcast interview he still has concerns about aspects of the bill pertaining to border security. But the Ohio Republican also said he has sought to create an environment in the House where both parties can work together on the measure, which could eventually lead to full citizenship for millions of people currently living in the United States illegally.

“I think, no question, by the end of the year we could have a bill. No question,” the speaker said in an interview on ABC’s “Good Morning America.”

In the Senate, the bill’s supporters were working to determine which measures they could accept to lock down more “yes” votes from the GOP side without losing Democratic backing. They are aiming for a resounding show of support from the Democratic-led Senate that could pressure the Republican-led House to act.

President Barack Obama, who’s made overhauling immigration laws a top second-term priority, was to speak at a midmorning event with advocates at the White House to praise the Senate’s efforts and renew his calls for reform.

The two votes scheduled for Tuesday afternoon were on procedural measures to officially allow debate to move forward on the far-reaching bill. Both votes were expected to succeed by comfortable margins, because even some senators with deep misgivings about the immigration bill said the issue deserved a Senate debate.

The real fights will come in the following days and weeks as Senate Majority Leader Harry Reid, D-Nev., aims to push the bill to final Senate passage before July 4.

Even if that happens, the outlook in the House remains unsettled. Boehner indicated earlier that he’d like to see a bill through his chamber before August.

The Senate bill would stiffen border security and require all employers to check their workers’ legal status, as well as initiate new or expanded visa programs for high-skilled and lower-skilled workers and the agriculture sector. At its core is its most contentious element, a 13-year path to citizenship for some 11 million immigrants now here illegally.

“Given the impact the broken system has on our economy and our families, we cannot afford delay,” Senate Judiciary Chairman Patrick Leahy, D-Vt., said Monday on the Senate floor. “This is a measure the Senate should come together to consider and pass.”

“Unfortunately the bill before us repeats our past mistakes,” said the Judiciary Committee’s top Republican, Sen. Chuck Grassley of Iowa. “Nobody disputes this is a bill that legalizes first and enforces later.”

Heated debate is anticipated on the border security elements of the bill. The bill sets up a system wherein immigrants may only begin taking steps toward citizenship once certain border security requirements are met. But opponents say those “triggers” aren’t strong enough, and one of the bill’s authors, Sen. Marco Rubio, R-Fla., has argued that the border security elements of the bill must be strengthened if it’s to make it through Congress.

An amendment announced by Sen. John Cornyn, R-Texas., would require 100 percent monitoring of the entire U.S.-Mexico border and 90 percent of would-be crossers to be stopped or turned back before anyone can get a permanent resident green card. The Senate bill, authored by a bipartisan group of eight senators, also sets those figures as goals, but doesn’t make the path to citizenship directly contingent on them.

“It’s time for us to adopt real triggers,” Cornyn said Monday. He said his measure was “essential to accomplishing the goal of bipartisan immigration reform.”

But in an interview over the weekend with Univision, Reid dismissed Cornyn’s amendment as a “poison pill.”

“If people have suggestions like they did in the Judiciary Committee to change the bill a little bit, I’ll be happy to take a look at that,” Reid said. “But we’re not going to have big changes in this legislation.”

It’s not likely to be Cornyn’s, but supporters of the bill were looking for a border security measure they could support. It could be an amendment pushed by Rubio, who’s talked about giving Congress a more direct role in developing a border security plan that the bill now leaves to the Homeland Security Department.

Other disputes will surround amendments being pushed by Sen. Orrin Hatch, R-Utah, to strengthen requirements for payment of back taxes in the bill and require previously illegal immigrants who get green cards under the bill to wait five years before beginning to access benefits under the nation’s new health care law.

(AP)