Comprehensive immigration reform is about to face another tough battle this week, as the Senate Judiciary Committee begins to mark up the bill. However, there is good news for the “gang of eight” senators who wrote the 2013 bill and are fighting to get it passed.

A new bipartisan survey found that 71 percent likely general election voters support passing an immigration reform bill similar to the one drafted by the eight senators. They favor a path to citizenship; allowing entry to more high-skilled workers and guest workers; increased border security; and e-verify requirements for employers. Only 20 percent of those polled oppose such reforms.

Democratic polling firm Global Strategy Group and Republican polling firm Basswood Research conducted the survey for, the new advocacy group co-founded by Facebook’s (NASDAQ:FB) Mark Zuckerberg. The survey of 1,232 people was done between April 20 and 24.

Here’s what researchers found:

-- In keeping with the spirit of the bipartisan work between four Republican senators and four Democrats to produce the immigration reform bill, officially known as Border Security, Economic Opportunity, and Immigration Modernization Act, a large percentage of conservative GOP (74 percent) and liberal Democrats (78 percent) support the comprehensive package. More than two-thirds of swing voters (67 percent) approve the measure;

-- Lawmakers who rally behind passing the comprehensive immigration reform could get a boost from the voting public: 42 percent of survey respondents said they would likely vote for candidates who throw their support behind the bill. Only 12 percent are less likely to do that, but a majority of Republicans (45 percent) and Democrats (51 percent) is more likely to back lawmakers who support the measure;

-- 91 percent of voters support employers verifying the immigration status of potential employees;

-- 81 percent support boosting border security;

-- 78 percent approve of a pathway to citizenship along with increasing border security (58 percent) or without any requirement at all (25 percent);

-- 66 percent want more high-skilled workers coming to America; and

-- 59 percent think more guest workers should be brought into the country.

“The inclusion of border security and numerous requirements before citizenship is an option makes the bipartisan U.S. Senate proposal supported by a larger margin among conservative Republicans than others,” said Republican pollster Jon Lerner in a statement, noting conservative Republicans are the most hostile to the current system.