On Friday night, most of the Democratic caucus in the Senate protested against the lack of legislative progress on fixing the DACA program by voting against cloture on a Republican continuing resolution (CR) funding the federal government through February 16, thus precipitating a government shutdown. On Monday, most Democrats joined Republicans in voting to reopen the government through February 8—having won an informal agreement that the Senate majority leader would bring an immigration reform bill to the floor if one is produced by a bipartisan working group of senators.
Compared to the original demands of Senate Democrats, the "deal" they struck to reopen the government didn't look like much of a victory. Compared to 1995-96 and 2013 (when Republicans got nothing but political pain out of two much longer shutdowns), winning a shorter CR, a public pledge by Mitch McConnell, and a six-year reauthorization of the CHIP program (included in both bills) seemed like a pretty decent haul. But the experience seems to have left feelings of dissatisfaction across much of the party; moderate Senate Democrats either opposed or reluctantly supported the shutdown in the first place, while some liberal activists complained that Democrats caved too early and thus revealed the shallowness of their sympathy to the plight of the DREAMers.
Extracting a big payoff from a shutdown is probably impossible in most cases, because the cost is borne not only by the political opposition (if at all) but also by the public at large. Even if they sympathize with the underlying objectives, citizens will soon start to wonder why they have to suffer the inconveniences associated with an unfunded government. For a party out of power, forcing a shutdown is somewhat like running out onto the field during a sporting event—it seems in the moment like a dramatic act of defiant self-assertion, but immediately upon execution reveals a limited consideration of the key question "so then what happens?"
It's true that most Americans support a solution that would allow the DREAMers to remain in the United States lawfully; it's equally true that most Republican politicians are reluctant (with good reason) to cast their votes in favor of any bill that could be characterized by a future primary opponent as constituting "amnesty for illegals." The main obstacle to successful bipartisan negotiations over the issue has been the long and growing list of concessions that Trump and other Republican leaders have demanded as a price for their support. But these demands in turn reflect a political reality in which risk for Republicans exists much more on one side of the issue than the other—and government shutdowns aren't likely to change those calculations much.
If the DACA expiration date of March 5 arrives without a deal, however, the Trump administration will have to decide what to do about the DREAMers. It's quite possible that Trump will choose not to prioritize immigration enforcement measures against those who have registered under DACA despite the program's nominal cessation; it's also possible that the administration's freedom to maneuver will be limited at least temporarily by legal action. But there's a reasonable chance that Trump, encouraged by the immigration hawks on his staff like White House senior policy advisor Stephen Miller, will preside over the deportation proceedings of significant numbers of DACA-eligible immigrants.
Polling suggests that such a development, if it occurs, would be unpopular with the public, and congressional Republicans already facing an electoral headwind in 2018 would not welcome a campaign season characterized by widespread media images of sympathetic DREAMers being detained by federal agents. Another president might be counted on to spare his party such politically difficult developments in an important election year, but Trump hardly enjoys the private trust of his fellow Republican officeholders. If a bipartisan DACA agreement is indeed successfully enacted into law—an improbable development, from today's vantage point—it is much more likely to reflect Republican fears of an untrammeled Trump than another shutdown showdown.